LMFDB - Embedded newform 18.11.d.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,11,Mod(5,18)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 11, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	18.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.4364305481$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 63819 x^{18} - 574086 x^{17} + 1685636151 x^{16} - 13472077884 x^{15} + \cdots + 42\!\cdots\!17 $ x^20 - 10x^19 + 63819x^18 - 574086x^17 + 1685636151x^16 - 13472077884x^15 + 23849722149866x^14 - 166712339223788x^13 + 195479019402402405x^12 - 1170707468814910094x^11 + 938326637750627487341x^10 - 4680905675328128110986x^9 + 2551316542474577226379677x^8 - 10177193606819996156162676x^7 + 3644946427174260203987635170x^6 - 10899238750832113741944409252x^5 + 2446510322689300614446071763767x^4 - 4874867111497712925857039900178x^3 + 623192578601325527612865828822963x^2 - 620756959890572838693596656972206*x + 42080692026395342189225080891718217
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{46}\cdot 3^{37} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.2
Root			$0.500000 - 100.759i$ of defining polynomial
Character	$\chi$	$=$	18.5
Dual form			18.11.d.a.11.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-19.5959 + 11.3137i) q^{2} +(-196.987 + 142.285i) q^{3} +(256.000 - 443.405i) q^{4} +(3091.89 + 1785.10i) q^{5} +(2250.37 - 5016.87i) q^{6} +(12604.4 + 21831.4i) q^{7} +11585.2i q^{8} +(18558.8 - 56056.7i) q^{9} -80784.5 q^{10} +(-171690. + 99125.1i) q^{11} +(12661.4 + 123770. i) q^{12} +(141992. - 245938. i) q^{13} +(-493988. - 285204. i) q^{14} +(-863055. + 88288.4i) q^{15} +(-131072. - 227023. i) q^{16} +1.47323e6i q^{17} +(270534. + 1.30845e6i) q^{18} -4.67704e6 q^{19} +(1.58305e6 - 913972. i) q^{20} +(-5.58918e6 - 2.50709e6i) q^{21} +(2.24294e6 - 3.88489e6i) q^{22} +(4.51953e6 + 2.60935e6i) q^{23} +(-1.64841e6 - 2.28214e6i) q^{24} +(1.49036e6 + 2.58138e6i) q^{25} +6.42584e6i q^{26} +(4.32022e6 + 1.36831e7i) q^{27} +1.29069e7 q^{28} +(1.64106e6 - 947468. i) q^{29} +(1.59135e7 - 1.14944e7i) q^{30} +(9.25805e6 - 1.60354e7i) q^{31} +(5.13695e6 + 2.96582e6i) q^{32} +(1.97166e7 - 4.39553e7i) q^{33} +(-1.66677e7 - 2.88693e7i) q^{34} +9.00003e7i q^{35} +(-2.01048e7 - 2.25796e7i) q^{36} -9.06055e7 q^{37} +(9.16509e7 - 5.29147e7i) q^{38} +(7.02273e6 + 6.86501e7i) q^{39} +(-2.06808e7 + 3.58202e7i) q^{40} +(-4.27366e6 - 2.46740e6i) q^{41} +(1.37890e8 - 1.41058e7i) q^{42} +(-3.66421e7 - 6.34660e7i) q^{43} +1.01504e8i q^{44} +(1.57449e8 - 1.40192e8i) q^{45} -1.18086e8 q^{46} +(-2.91846e8 + 1.68497e8i) q^{47} +(5.81216e7 + 2.60710e7i) q^{48} +(-1.76502e8 + 3.05711e8i) q^{49} +(-5.84101e7 - 3.37231e7i) q^{50} +(-2.09619e8 - 2.90207e8i) q^{51} +(-7.27001e7 - 1.25920e8i) q^{52} +8.02924e7i q^{53} +(-2.39465e8 - 2.19255e8i) q^{54} -7.07793e8 q^{55} +(-2.52922e8 + 1.46025e8i) q^{56} +(9.21316e8 - 6.65475e8i) q^{57} +(-2.14388e7 + 3.71330e7i) q^{58} +(7.95473e8 + 4.59267e8i) q^{59} +(-1.81795e8 + 4.05285e8i) q^{60} +(3.70068e6 + 6.40977e6i) q^{61} +4.18972e8i q^{62} +(1.45772e9 - 3.01396e8i) q^{63} -1.34218e8 q^{64} +(8.78049e8 - 5.06942e8i) q^{65} +(1.10933e8 + 1.08441e9i) q^{66} +(9.55400e8 - 1.65480e9i) q^{67} +(6.53238e8 + 3.77147e8i) q^{68} +(-1.26156e9 + 1.29055e8i) q^{69} +(-1.01824e9 - 1.76364e9i) q^{70} +2.72418e9i q^{71} +(6.49431e8 + 2.15008e8i) q^{72} +2.42985e9 q^{73} +(1.77550e9 - 1.02508e9i) q^{74} +(-6.60875e8 - 2.96442e8i) q^{75} +(-1.19732e9 + 2.07382e9i) q^{76} +(-4.32808e9 - 2.49882e9i) q^{77} +(-9.14303e8 - 1.26581e9i) q^{78} +(7.42978e8 + 1.28688e9i) q^{79} -9.35907e8i q^{80} +(-2.79793e9 - 2.08069e9i) q^{81} +1.11662e8 q^{82} +(-5.66479e8 + 3.27057e8i) q^{83} +(-2.54249e9 + 1.83646e9i) q^{84} +(-2.62987e9 + 4.55506e9i) q^{85} +(1.43607e9 + 8.29117e8i) q^{86} +(-1.88457e8 + 4.20138e8i) q^{87} +(-1.14839e9 - 1.98907e9i) q^{88} -1.33310e9i q^{89} +(-1.49926e9 + 4.52851e9i) q^{90} +7.15890e9 q^{91} +(2.31400e9 - 1.33599e9i) q^{92} +(4.57889e8 + 4.47605e9i) q^{93} +(3.81266e9 - 6.60372e9i) q^{94} +(-1.44609e10 - 8.34899e9i) q^{95} +(-1.43391e9 + 1.46685e8i) q^{96} +(2.78067e9 + 4.81625e9i) q^{97} -7.98759e9i q^{98} +(2.37028e9 + 1.14640e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 84 q^{3} + 5120 q^{4} - 9918 q^{5} + 12864 q^{6} + 12238 q^{7} + 79248 q^{9} - 327582 q^{11} + 9216 q^{12} - 280550 q^{13} + 175680 q^{14} - 2685042 q^{15} - 2621440 q^{16} + 3925632 q^{18} - 2966240 q^{19}+ \cdots + 41160676842 q^{99}+O(q^{100}) $ 20 * q - 84 * q^3 + 5120 * q^4 - 9918 * q^5 + 12864 * q^6 + 12238 * q^7 + 79248 * q^9 - 327582 * q^11 + 9216 * q^12 - 280550 * q^13 + 175680 * q^14 - 2685042 * q^15 - 2621440 * q^16 + 3925632 * q^18 - 2966240 * q^19 - 5078016 * q^20 - 11895726 * q^21 + 3473472 * q^22 + 10446606 * q^23 + 2752512 * q^24 + 9609944 * q^25 + 2340576 * q^27 + 12531712 * q^28 + 32440806 * q^29 + 37556352 * q^30 - 40069958 * q^31 - 35367930 * q^33 + 30746496 * q^34 - 32695296 * q^36 - 127390400 * q^37 + 370567296 * q^38 + 153125550 * q^39 - 245419398 * q^41 - 344505600 * q^42 - 86593094 * q^43 + 394622766 * q^45 - 366913920 * q^46 + 1094979330 * q^47 + 26738688 * q^48 - 598072056 * q^49 - 456606720 * q^50 - 2329772724 * q^51 + 143641600 * q^52 + 1623484224 * q^54 - 262510308 * q^55 + 89948160 * q^56 + 311135772 * q^57 + 249515904 * q^58 - 2125085130 * q^59 - 2357738496 * q^60 + 312021586 * q^61 + 5475513858 * q^63 - 2684354560 * q^64 + 13076821350 * q^65 + 2185467264 * q^66 - 1200881210 * q^67 - 2610487296 * q^68 - 11765922354 * q^69 + 1138681152 * q^70 + 1554382848 * q^72 + 5213376328 * q^73 + 9118122624 * q^74 + 13244996208 * q^75 - 759357440 * q^76 - 33678720774 * q^77 - 14572366080 * q^78 - 3396212726 * q^79 + 14546869128 * q^81 + 3667214592 * q^82 + 16739541378 * q^83 + 1518514176 * q^84 + 7141101588 * q^85 - 11512304064 * q^86 - 32778228834 * q^87 - 1778417664 * q^88 + 16769410560 * q^90 - 10426841884 * q^91 + 5348662272 * q^92 - 4843832814 * q^93 + 6416128320 * q^94 - 26494427340 * q^95 - 1962934272 * q^96 + 6721893598 * q^97 + 41160676842 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−19.5959	+	11.3137i	−0.612372	+	0.353553i
$2$	−19.5959	+	11.3137i	−0.612372	+	0.353553i
$3$	−196.987	+	142.285i	−0.810646	+	0.585536i
$3$	−196.987	+	142.285i	−0.810646	+	0.585536i
$4$	256.000	−	443.405i	0.250000	−	0.433013i
$5$	3091.89	+	1785.10i	0.989404	+	0.571233i	0.905096	−	0.425207i	$-0.139799\pi$
$5$	3091.89	+	1785.10i	0.989404	+	0.571233i	0.0843077	+	0.996440i	$0.473132\pi$
$6$	2250.37	−	5016.87i	0.289399	−	0.645173i
$7$	12604.4	+	21831.4i	0.749947	+	1.29895i	0.947847	+	0.318725i	$0.103255\pi$
$7$	12604.4	+	21831.4i	0.749947	+	1.29895i	−0.197900	+	0.980222i	$0.563412\pi$
$8$			11585.2i			0.353553i
$9$	18558.8	−	56056.7i	0.314294	−	0.949326i
$10$	−80784.5			−0.807845
$11$	−171690.	+	99125.1i	−1.06606	+	0.615489i	−0.927102	−	0.374810i	$-0.877708\pi$
$11$	−171690.	+	99125.1i	−1.06606	+	0.615489i	−0.138956	+	0.990299i	$0.544375\pi$
$12$	12661.4	+	123770.i	0.0508832	+	0.497404i
$13$	141992.	−	245938.i	0.382427	−	0.662383i	−0.608982	−	0.793184i	$-0.708422\pi$
$13$	141992.	−	245938.i	0.382427	−	0.662383i	0.991409	+	0.130801i	$0.0417550\pi$
$14$	−493988.	−	285204.i	−0.918494	−	0.530293i
$15$	−863055.	+	88288.4i	−1.13653	+	0.116265i
$16$	−131072.	−	227023.i	−0.125000	−	0.216506i
$17$			1.47323e6i			1.03759i	0.854899	+	0.518795i	$0.173619\pi$
$17$			1.47323e6i			1.03759i	−0.854899	+	0.518795i	$0.826381\pi$
$18$	270534.	+	1.30845e6i	0.143172	+	0.692461i
$19$	−4.67704e6			−1.88888			−0.944438	−	0.328691i	$-0.893393\pi$
$19$	−4.67704e6			−1.88888			−0.944438	+	0.328691i	$0.893393\pi$
$20$	1.58305e6	−	913972.i	0.494702	−	0.285616i
$21$	−5.58918e6	−	2.50709e6i	−1.36852	−	0.613865i
$22$	2.24294e6	−	3.88489e6i	0.435216	−	0.753817i
$23$	4.51953e6	+	2.60935e6i	0.702190	+	0.405409i	0.808162	−	0.588960i	$-0.200462\pi$
$23$	4.51953e6	+	2.60935e6i	0.702190	+	0.405409i	−0.105973	+	0.994369i	$0.533796\pi$
$24$	−1.64841e6	−	2.28214e6i	−0.207018	−	0.286607i
$25$	1.49036e6	+	2.58138e6i	0.152613	+	0.264334i
$26$			6.42584e6i			0.540833i
$27$	4.32022e6	+	1.36831e7i	0.301083	+	0.953598i
$28$	1.29069e7			0.749947
$29$	1.64106e6	−	947468.i	0.0800083	−	0.0461928i	−0.459462	−	0.888197i	$-0.651958\pi$
$29$	1.64106e6	−	947468.i	0.0800083	−	0.0461928i	0.539470	+	0.842005i	$0.318624\pi$
$30$	1.59135e7	−	1.14944e7i	0.654876	−	0.473023i
$31$	9.25805e6	−	1.60354e7i	0.323378	−	0.560108i	−0.657804	−	0.753189i	$-0.728515\pi$
$31$	9.25805e6	−	1.60354e7i	0.323378	−	0.560108i	0.981183	+	0.193081i	$0.0618480\pi$
$32$	5.13695e6	+	2.96582e6i	0.153093	+	0.0883883i
$33$	1.97166e7	−	4.39553e7i	0.503805	−	1.12316i
$34$	−1.66677e7	−	2.88693e7i	−0.366844	−	0.635392i
$35$			9.00003e7i			1.71358i
$36$	−2.01048e7	−	2.25796e7i	−0.332497	−	0.373425i
$37$	−9.06055e7			−1.30661			−0.653305	−	0.757095i	$-0.726618\pi$
$37$	−9.06055e7			−1.30661			−0.653305	+	0.757095i	$0.726618\pi$
$38$	9.16509e7	−	5.29147e7i	1.15670	−	0.667818i
$39$	7.02273e6	+	6.86501e7i	0.0778364	+	0.760883i
$40$	−2.06808e7	+	3.58202e7i	−0.201961	+	0.349807i
$41$	−4.27366e6	−	2.46740e6i	−0.0368876	−	0.0212971i	0.481443	−	0.876478i	$-0.340113\pi$
$41$	−4.27366e6	−	2.46740e6i	−0.0368876	−	0.0212971i	−0.518330	+	0.855180i	$0.673446\pi$
$42$	1.37890e8	−	1.41058e7i	1.05508	−	0.107932i
$43$	−3.66421e7	−	6.34660e7i	−0.249252	−	0.431717i	0.714067	−	0.700078i	$-0.246851\pi$
$43$	−3.66421e7	−	6.34660e7i	−0.249252	−	0.431717i	−0.963318	+	0.268361i	$0.913518\pi$
$44$			1.01504e8i			0.615489i
$45$	1.57449e8	−	1.40192e8i	0.853249	−	0.759731i
$46$	−1.18086e8			−0.573335
$47$	−2.91846e8	+	1.68497e8i	−1.27252	+	0.734689i	−0.975461	−	0.220170i	$-0.929339\pi$
$47$	−2.91846e8	+	1.68497e8i	−1.27252	+	0.734689i	−0.297058	+	0.954860i	$0.596005\pi$
$48$	5.81216e7	+	2.60710e7i	0.228103	+	0.102318i
$49$	−1.76502e8	+	3.05711e8i	−0.624842	+	1.08226i
$50$	−5.84101e7	−	3.37231e7i	−0.186912	−	0.107914i
$51$	−2.09619e8	−	2.90207e8i	−0.607547	−	0.841119i
$52$	−7.27001e7	−	1.25920e8i	−0.191213	−	0.331191i
$53$			8.02924e7i			0.191997i	0.995381	+	0.0959986i	$0.0306044\pi$
$53$			8.02924e7i			0.191997i	−0.995381	+	0.0959986i	$0.969396\pi$
$54$	−2.39465e8	−	2.19255e8i	−0.521523	−	0.477508i
$55$	−7.07793e8			−1.40635
$56$	−2.52922e8	+	1.46025e8i	−0.459247	+	0.265146i
$57$	9.21316e8	−	6.65475e8i	1.53121	−	1.10601i
$58$	−2.14388e7	+	3.71330e7i	−0.0326633	+	0.0565744i
$59$	7.95473e8	+	4.59267e8i	1.11267	+	0.642399i	0.939519	−	0.342497i	$-0.111273\pi$
$59$	7.95473e8	+	4.59267e8i	1.11267	+	0.642399i	0.173149	+	0.984896i	$0.444606\pi$
$60$	−1.81795e8	+	4.05285e8i	−0.233789	+	0.521200i
$61$	3.70068e6	+	6.40977e6i	0.00438160	+	0.00758915i	0.868208	−	0.496201i	$-0.165272\pi$
$61$	3.70068e6	+	6.40977e6i	0.00438160	+	0.00758915i	−0.863826	+	0.503790i	$0.831939\pi$
$62$			4.18972e8i			0.457326i
$63$	1.45772e9	−	3.01396e8i	1.46883	−	0.303693i
$64$	−1.34218e8			−0.125000
$65$	8.78049e8	−	5.06942e8i	0.756749	−	0.436909i
$66$	1.10933e8	+	1.08441e9i	0.0885808	+	0.865914i
$67$	9.55400e8	−	1.65480e9i	0.707638	−	1.22566i	−0.258093	−	0.966120i	$-0.583094\pi$
$67$	9.55400e8	−	1.65480e9i	0.707638	−	1.22566i	0.965731	−	0.259545i	$-0.0835724\pi$
$68$	6.53238e8	+	3.77147e8i	0.449290	+	0.259398i
$69$	−1.26156e9	+	1.29055e8i	−0.806609	+	0.0825141i
$70$	−1.01824e9	−	1.76364e9i	−0.605841	−	1.04935i
$71$			2.72418e9i			1.50989i	0.655790	+	0.754943i	$0.272336\pi$
$71$			2.72418e9i			1.50989i	−0.655790	+	0.754943i	$0.727664\pi$
$72$	6.49431e8	+	2.15008e8i	0.335637	+	0.111120i
$73$	2.42985e9			1.17210			0.586051	−	0.810274i	$-0.300682\pi$
$73$	2.42985e9			1.17210			0.586051	+	0.810274i	$0.300682\pi$
$74$	1.77550e9	−	1.02508e9i	0.800132	−	0.461956i
$75$	−6.60875e8	−	2.96442e8i	−0.278492	−	0.124921i
$76$	−1.19732e9	+	2.07382e9i	−0.472219	+	0.817907i
$77$	−4.32808e9	−	2.49882e9i	−1.59897	−	0.923168i
$78$	−9.14303e8	−	1.26581e9i	−0.316678	−	0.438424i
$79$	7.42978e8	+	1.28688e9i	0.241457	+	0.418217i	0.961130	−	0.276097i	$-0.0890412\pi$
$79$	7.42978e8	+	1.28688e9i	0.241457	+	0.418217i	−0.719672	+	0.694314i	$0.755708\pi$
$80$		−	9.35907e8i		−	0.285616i
$81$	−2.79793e9	−	2.08069e9i	−0.802438	−	0.596735i
$82$	1.11662e8			0.0301186
$83$	−5.66479e8	+	3.27057e8i	−0.143811	+	0.0830295i	−0.570179	−	0.821520i	$-0.693126\pi$
$83$	−5.66479e8	+	3.27057e8i	−0.143811	+	0.0830295i	0.426368	+	0.904550i	$0.359793\pi$
$84$	−2.54249e9	+	1.83646e9i	−0.607942	+	0.439121i
$85$	−2.62987e9	+	4.55506e9i	−0.592705	+	1.02660i
$86$	1.43607e9	+	8.29117e8i	0.305270	+	0.176248i
$87$	−1.88457e8	+	4.20138e8i	−0.0378109	+	0.0842938i
$88$	−1.14839e9	−	1.98907e9i	−0.217608	−	0.376908i
$89$		−	1.33310e9i		−	0.238733i	−0.992850	−	0.119366i	$-0.961914\pi$
$89$		−	1.33310e9i		−	0.238733i	0.992850	−	0.119366i	$-0.0380863\pi$
$90$	−1.49926e9	+	4.52851e9i	−0.253901	+	0.766908i
$91$	7.15890e9			1.14720
$92$	2.31400e9	−	1.33599e9i	0.351095	−	0.202705i
$93$	4.57889e8	+	4.47605e9i	0.0658181	+	0.643399i
$94$	3.81266e9	−	6.60372e9i	0.519504	−	0.899807i
$95$	−1.44609e10	−	8.34899e9i	−1.86886	−	1.07899i
$96$	−1.43391e9	+	1.46685e8i	−0.175859	+	0.0179899i
$97$	2.78067e9	+	4.81625e9i	0.323810	+	0.560855i	0.981271	−	0.192634i	$-0.0617029\pi$
$97$	2.78067e9	+	4.81625e9i	0.323810	+	0.560855i	−0.657461	+	0.753489i	$0.728370\pi$
$98$		−	7.98759e9i		−	0.883660i
$99$	2.37028e9	+	1.14640e10i	0.249244	+	1.20548i
$100$	1.52613e9			0.152613
$101$	1.81497e9	−	1.04787e9i	0.172688	−	0.0997015i	−0.411165	−	0.911561i	$-0.634878\pi$
$101$	1.81497e9	−	1.04787e9i	0.172688	−	0.0997015i	0.583853	+	0.811860i	$0.301545\pi$
$102$	7.39100e9	+	3.31531e9i	0.669425	+	0.300278i
$103$	−6.89443e9	+	1.19415e10i	−0.594720	+	1.03008i	0.398867	+	0.917009i	$0.369404\pi$
$103$	−6.89443e9	+	1.19415e10i	−0.594720	+	1.03008i	−0.993586	+	0.113076i	$0.963930\pi$
$104$	2.84925e9	+	1.64502e9i	0.234188	+	0.135208i
$105$	−1.28057e10	−	1.77289e10i	−1.00336	−	1.38910i
$106$	−9.08405e8	−	1.57340e9i	−0.0678813	−	0.117574i
$107$		−	2.70745e9i		−	0.193037i	−0.995331	−	0.0965186i	$-0.969229\pi$
$107$		−	2.70745e9i		−	0.193037i	0.995331	−	0.0965186i	$-0.0307707\pi$
$108$	7.17312e9	+	1.58726e9i	0.488191	+	0.108027i
$109$	2.29489e10			1.49152			0.745760	−	0.666215i	$-0.232087\pi$
$109$	2.29489e10			1.49152			0.745760	+	0.666215i	$0.232087\pi$
$110$	1.38699e10	−	8.00777e9i	0.861209	−	0.497219i
$111$	1.78481e10	−	1.28918e10i	1.05920	−	0.765067i
$112$	3.30416e9	−	5.72297e9i	0.187487	−	0.324737i
$113$	5.53357e9	+	3.19481e9i	0.300340	+	0.173401i	0.642596	−	0.766206i	$-0.277858\pi$
$113$	5.53357e9	+	3.19481e9i	0.300340	+	0.173401i	−0.342256	+	0.939607i	$0.611191\pi$
$114$	−1.05251e10	+	2.34641e10i	−0.546638	+	1.21865i
$115$	9.31592e9	+	1.61357e10i	0.463166	+	0.802227i
$116$		−	9.70207e8i		−	0.0461928i
$117$	−1.11513e10	−	1.25239e10i	−0.508622	−	0.571231i
$118$	−2.07840e10			−0.908489
$119$	−3.21627e10	+	1.85691e10i	−1.34777	+	0.778138i
$120$	−1.02284e9	−	9.99870e9i	−0.0411057	−	0.401825i
$121$	6.68286e9	−	1.15750e10i	0.257653	−	0.446268i
$122$	−1.45036e8	−	8.37368e7i	−0.00536634	−	0.00309826i
$123$	1.19293e9	−	1.22034e8i	0.0423730	−	0.00433465i
$124$	−4.74012e9	−	8.21013e9i	−0.161689	−	0.280054i
$125$		−	2.42235e10i		−	0.793755i
$126$	−2.51554e10	+	2.23983e10i	−0.792098	+	0.705282i
$127$	2.33830e10			0.707752			0.353876	−	0.935292i	$-0.384863\pi$
$127$	2.33830e10			0.707752			0.353876	+	0.935292i	$0.384863\pi$
$128$	2.63012e9	−	1.51850e9i	0.0765466	−	0.0441942i
$129$	1.62483e10	+	7.28835e9i	0.454841	+	0.204024i
$130$	−1.14708e10	+	1.98680e10i	−0.308942	+	0.535102i
$131$	5.53612e10	+	3.19628e10i	1.43499	+	0.828493i	0.997496	−	0.0707280i	$-0.0225322\pi$
$131$	5.53612e10	+	3.19628e10i	1.43499	+	0.828493i	0.437496	+	0.899221i	$0.355866\pi$
$132$	−1.44425e10	−	1.99950e10i	−0.360391	−	0.498944i
$133$	−5.89511e10	−	1.02106e11i	−1.41656	−	2.45355i
$134$			4.32364e10i			1.00075i
$135$	−1.10681e10	+	5.00186e10i	−0.246833	+	1.11548i
$136$	−1.70677e10			−0.366844
$137$	−1.92851e10	+	1.11342e10i	−0.399593	+	0.230705i	−0.686309	−	0.727311i	$-0.740770\pi$
$137$	−1.92851e10	+	1.11342e10i	−0.399593	+	0.230705i	0.286715	+	0.958016i	$0.407437\pi$
$138$	2.32614e10	−	1.68019e10i	0.464772	−	0.335709i
$139$	−4.79695e10	+	8.30856e10i	−0.924466	+	1.60122i	−0.132048	+	0.991243i	$0.542155\pi$
$139$	−4.79695e10	+	8.30856e10i	−0.924466	+	1.60122i	−0.792418	+	0.609979i	$0.791178\pi$
$140$	3.99066e10	+	2.30401e10i	0.742001	+	0.428394i
$141$	3.35152e10	−	7.47172e10i	0.601375	−	1.34068i
$142$	−3.08206e10	−	5.33828e10i	−0.533825	−	0.924613i
$143$			5.63001e10i			0.941518i
$144$	−1.51587e10	+	3.13420e9i	−0.244822	+	0.0506190i
$145$	6.76531e9			0.105547
$146$	−4.76152e10	+	2.74906e10i	−0.717763	+	0.414401i
$147$	−8.72953e9	−	8.53348e10i	−0.127176	−	1.24320i
$148$	−2.31950e10	+	4.01749e10i	−0.326652	+	0.565779i
$149$	−6.42829e10	−	3.71137e10i	−0.875314	−	0.505363i	−0.00620357	−	0.999981i	$-0.501975\pi$
$149$	−6.42829e10	−	3.71137e10i	−0.875314	−	0.505363i	−0.869111	+	0.494618i	$0.835308\pi$
$150$	1.63043e10	−	1.66789e9i	0.214707	−	0.0219640i
$151$	−2.26560e10	−	3.92414e10i	−0.288602	−	0.499873i	0.684875	−	0.728661i	$-0.259857\pi$
$151$	−2.26560e10	−	3.92414e10i	−0.288602	−	0.499873i	−0.973476	+	0.228788i	$0.926524\pi$
$152$		−	5.41846e10i		−	0.667818i
$153$	8.25845e10	+	2.73413e10i	0.985011	+	0.326109i
$154$	1.13084e11			1.30556
$155$	5.72497e10	−	3.30531e10i	0.639904	−	0.369449i
$156$	3.22376e10	+	1.44605e10i	0.348931	+	0.156517i
$157$	−1.81100e10	+	3.13674e10i	−0.189854	+	0.328837i	−0.945201	−	0.326488i	$-0.894135\pi$
$157$	−1.81100e10	+	3.13674e10i	−0.189854	+	0.328837i	0.755347	+	0.655325i	$0.227468\pi$
$158$	−2.91187e10	−	1.68117e10i	−0.295724	−	0.170736i
$159$	−1.14244e10	−	1.58166e10i	−0.112421	−	0.155642i
$160$	1.05886e10	+	1.83400e10i	0.100981	+	0.174904i
$161$			1.31557e11i			1.21614i
$162$	7.83683e10	+	9.11800e9i	0.702369	+	0.0817193i
$163$	1.39750e10			0.121455			0.0607273	−	0.998154i	$-0.480658\pi$
$163$	1.39750e10			0.121455			0.0607273	+	0.998154i	$0.480658\pi$
$164$	−2.18811e9	+	1.26331e9i	−0.0184438	+	0.0106485i
$165$	1.39426e11	−	1.00709e11i	1.14005	−	0.823469i
$166$	7.40045e9	−	1.28180e10i	0.0587107	−	0.101690i
$167$	1.29494e11	+	7.47632e10i	0.996933	+	0.575580i	0.907339	−	0.420399i	$-0.138110\pi$
$167$	1.29494e11	+	7.47632e10i	0.996933	+	0.575580i	0.0895936	+	0.995978i	$0.471443\pi$
$168$	2.90452e10	−	6.47520e10i	0.217034	−	0.483846i
$169$	2.86055e10	+	4.95463e10i	0.207499	+	0.359399i
$170$		−	1.19014e11i		−	0.838212i
$171$	−8.68001e10	+	2.62180e11i	−0.593662	+	1.79316i
$172$	−3.75215e10			−0.249252
$173$	1.06275e11	−	6.13581e10i	0.685807	−	0.395951i	−0.116233	−	0.993222i	$-0.537082\pi$
$173$	1.06275e11	−	6.13581e10i	0.685807	−	0.395951i	0.802039	+	0.597271i	$0.203748\pi$
$174$	−1.06033e9	−	1.03651e10i	−0.00664804	−	0.0649874i
$175$	−3.75701e10	+	6.50734e10i	−0.228904	+	0.396473i
$176$	4.50074e10	+	2.59850e10i	0.266514	+	0.153872i
$177$	−2.22045e11	+	2.27146e10i	−1.27813	+	0.130749i
$178$	1.50823e10	+	2.61233e10i	0.0844047	+	0.146193i
$179$		−	2.85929e11i		−	1.55594i	−0.628302	−	0.777969i	$-0.716250\pi$
$179$		−	2.85929e11i		−	1.55594i	0.628302	−	0.777969i	$-0.283750\pi$
$180$	−2.18549e10	−	1.05703e11i	−0.115661	−	0.559401i
$181$	−1.54643e11			−0.796045			−0.398022	−	0.917376i	$-0.630303\pi$
$181$	−1.54643e11			−0.796045			−0.398022	+	0.917376i	$0.630303\pi$
$182$	−1.40285e11	+	8.09937e10i	−0.702514	+	0.405596i
$183$	−1.64100e9	−	7.36088e8i	−0.00799565	−	0.00358653i
$184$	−3.02300e10	+	5.23599e10i	−0.143334	+	0.248261i
$185$	−2.80142e11	−	1.61740e11i	−1.29276	−	0.746378i
$186$	−5.96135e10	−	8.25320e10i	−0.267781	−	0.370730i
$187$	−1.46034e11	−	2.52938e11i	−0.638625	−	1.10613i
$188$			1.72541e11i			0.734689i
$189$	−2.44267e11	+	2.66783e11i	−1.01288	+	1.10624i
$190$	3.77832e11			1.52592
$191$	−1.72218e11	+	9.94299e10i	−0.677502	+	0.391156i	−0.798913	−	0.601446i	$-0.794591\pi$
$191$	−1.72218e11	+	9.94299e10i	−0.677502	+	0.391156i	0.121411	+	0.992602i	$0.461258\pi$
$192$	2.64391e10	−	1.90972e10i	0.101331	−	0.0731921i
$193$	7.31637e10	−	1.26723e11i	0.273218	−	0.473227i	−0.696466	−	0.717590i	$-0.745245\pi$
$193$	7.31637e10	−	1.26723e11i	0.273218	−	0.473227i	0.969684	+	0.244363i	$0.0785787\pi$
$194$	−1.08979e11	−	6.29193e10i	−0.396584	−	0.228968i
$195$	−1.00834e11	+	2.24794e11i	−0.357629	+	0.797283i
$196$	9.03692e10	+	1.56524e11i	0.312421	+	0.541129i
$197$			1.34679e11i			0.453909i	0.973905	+	0.226955i	$0.0728769\pi$
$197$			1.34679e11i			0.453909i	−0.973905	+	0.226955i	$0.927123\pi$
$198$	−1.76148e11	−	1.97831e11i	−0.578832	−	0.650082i
$199$	4.99786e11			1.60147			0.800734	−	0.599020i	$-0.204443\pi$
$199$	4.99786e11			1.60147			0.800734	+	0.599020i	$0.204443\pi$
$200$	−2.99059e10	+	1.72662e10i	−0.0934561	+	0.0539569i
$201$	4.72526e10	+	4.61914e11i	0.144027	+	1.40793i
$202$	−2.37107e10	+	4.10681e10i	−0.0704996	+	0.122109i
$203$	4.13691e10	+	2.38845e10i	0.120004	+	0.0692844i
$204$	−1.82342e11	+	1.86531e10i	−0.516102	+	0.0527959i
$205$	−8.80912e9	−	1.52578e10i	−0.0243312	−	0.0421428i
$206$		−	3.12006e11i		−	0.841060i
$207$	2.30149e11	−	2.04924e11i	0.605560	−	0.539189i
$208$	−7.44449e10			−0.191213
$209$	8.03000e11	−	4.63612e11i	2.01365	−	1.16258i
$210$	4.51519e11	+	2.02534e11i	1.10555	+	0.495907i
$211$	−2.75783e10	+	4.77671e10i	−0.0659410	+	0.114213i	−0.897111	−	0.441805i	$-0.854338\pi$
$211$	−2.75783e10	+	4.77671e10i	−0.0659410	+	0.114213i	0.831170	+	0.556018i	$0.187672\pi$
$212$	3.56020e10	+	2.05548e10i	0.0831372	+	0.0479993i
$213$	−3.87611e11	−	5.36628e11i	−0.884093	−	1.22398i
$214$	3.06313e10	+	5.30549e10i	0.0682489	+	0.118211i
$215$		−	2.61640e11i		−	0.569523i
$216$	−1.58522e11	+	5.00507e10i	−0.337148	+	0.106449i
$217$	4.66767e11			0.970067
$218$	−4.49704e11	+	2.59637e11i	−0.913366	+	0.527332i
$219$	−4.78649e11	+	3.45732e11i	−0.950160	+	0.686308i
$220$	−1.81195e11	+	3.13839e11i	−0.351587	+	0.608967i
$221$	3.62323e11	+	2.09188e11i	0.687282	+	0.396803i
$222$	−2.03895e11	+	4.54555e11i	−0.378131	+	0.842989i
$223$	−6.13593e10	−	1.06277e11i	−0.111264	−	0.192716i	0.805016	−	0.593253i	$-0.202157\pi$
$223$	−6.13593e10	−	1.06277e11i	−0.111264	−	0.192716i	−0.916280	+	0.400538i	$0.868823\pi$
$224$			1.49529e11i			0.265146i
$225$	1.72363e11	−	3.56376e10i	0.298904	−	0.0618010i
$226$	−1.44580e11			−0.245226
$227$	5.62176e11	−	3.24573e11i	0.932703	−	0.538496i	0.0450373	−	0.998985i	$-0.485659\pi$
$227$	5.62176e11	−	3.24573e11i	0.932703	−	0.538496i	0.887665	+	0.460489i	$0.152326\pi$
$228$	−5.92177e10	−	5.78878e11i	−0.0961120	−	0.939534i
$229$	3.14128e11	−	5.44085e11i	0.498803	−	0.863951i	−0.501197	−	0.865333i	$-0.667107\pi$
$229$	3.14128e11	−	5.44085e11i	0.498803	−	0.863951i	0.999999	+	0.00138219i	$0.000439964\pi$
$230$	−3.65108e11	−	2.10795e11i	−0.567260	−	0.327508i
$231$	1.20812e12	−	1.23588e11i	1.83675	−	0.187895i
$232$	1.09766e10	+	1.90121e10i	0.0163316	+	0.0282872i
$233$			5.57291e11i			0.811527i	0.913978	+	0.405763i	$0.132994\pi$
$233$			5.57291e11i			0.811527i	−0.913978	+	0.405763i	$0.867006\pi$
$234$	3.60212e11	+	1.19256e11i	0.513427	+	0.169981i
$235$	−1.20314e12			−1.67871
$236$	4.07282e11	−	2.35145e11i	0.556334	−	0.321199i
$237$	−3.29461e11	−	1.47783e11i	−0.440618	−	0.197644i
$238$	4.20171e11	−	7.27758e11i	0.550227	−	0.953021i
$239$	−1.20254e12	−	6.94289e11i	−1.54210	−	0.890329i	−0.998706	−	0.0508484i	$-0.983807\pi$
$239$	−1.20254e12	−	6.94289e11i	−1.54210	−	0.890329i	−0.543389	−	0.839481i	$-0.682859\pi$
$240$	1.33166e11	+	1.84362e11i	0.167239	+	0.231534i
$241$	5.39136e11	+	9.33810e11i	0.663152	+	1.14861i	0.979783	+	0.200063i	$0.0641148\pi$
$241$	5.39136e11	+	9.33810e11i	0.663152	+	1.14861i	−0.316631	+	0.948549i	$0.602552\pi$
$242$			3.02432e11i			0.364376i
$243$	8.47207e11	+	1.17638e10i	0.999904	+	0.0138840i
$244$	3.78950e9			0.00438160
$245$	−1.09145e12	+	6.30149e11i	−1.23644	+	0.713860i
$246$	−2.19959e10	+	1.58878e10i	−0.0244155	+	0.0176356i
$247$	−6.64105e11	+	1.15026e12i	−0.722357	+	1.25116i
$248$	1.85774e11	+	1.07257e11i	0.198028	+	0.114332i
$249$	6.50536e10	−	1.45028e11i	0.0679633	−	0.151514i
$250$	2.74057e11	+	4.74681e11i	0.280635	+	0.486073i
$251$			1.05338e12i			1.05734i	0.848827	+	0.528670i	$0.177309\pi$
$251$			1.05338e12i			1.05734i	−0.848827	+	0.528670i	$0.822691\pi$
$252$	2.39535e11	−	7.23517e11i	0.235704	−	0.711944i
$253$	−1.03461e12			−0.998100
$254$	−4.58211e11	+	2.64548e11i	−0.433408	+	0.250228i
$255$	−1.30069e11	−	1.27148e12i	−0.120635	−	1.17926i
$256$	−3.43597e10	+	5.95128e10i	−0.0312500	+	0.0541266i
$257$	9.27087e10	+	5.35254e10i	0.0826904	+	0.0477413i	0.540775	−	0.841167i	$-0.318131\pi$
$257$	9.27087e10	+	5.35254e10i	0.0826904	+	0.0477413i	−0.458085	+	0.888909i	$0.651464\pi$
$258$	−4.00859e11	+	4.10068e10i	−0.350665	+	0.0358722i
$259$	−1.14202e12	−	1.97804e12i	−0.979888	−	1.69722i
$260$		−	5.19108e11i		−	0.436909i
$261$	−2.26559e10	−	1.09576e11i	−0.0187059	−	0.0904721i
$262$	−1.44647e12			−1.17167
$263$	5.25464e11	−	3.03377e11i	0.417603	−	0.241103i	−0.276448	−	0.961029i	$-0.589157\pi$
$263$	5.25464e11	−	3.03377e11i	0.417603	−	0.241103i	0.694051	+	0.719925i	$0.255824\pi$
$264$	5.09232e11	+	2.28421e11i	0.397097	+	0.178122i
$265$	−1.43330e11	+	2.48255e11i	−0.109675	+	0.189963i
$266$	2.31040e12	+	1.33391e12i	1.73492	+	1.00166i
$267$	1.89680e11	+	2.62603e11i	0.139787	+	0.193528i
$268$	−4.89165e11	−	8.47258e11i	−0.353819	−	0.612832i
$269$			1.85533e12i			1.31722i	0.752483	+	0.658612i	$0.228856\pi$
$269$			1.85533e12i			1.31722i	−0.752483	+	0.658612i	$0.771144\pi$
$270$	−3.49007e11	−	1.10538e12i	−0.243229	−	0.770359i
$271$	5.55952e11			0.380357			0.190178	−	0.981750i	$-0.439093\pi$
$271$	5.55952e11			0.380357			0.190178	+	0.981750i	$0.439093\pi$
$272$	3.34458e11	−	1.93099e11i	0.224645	−	0.129699i
$273$	−1.41021e12	+	1.01861e12i	−0.929973	+	0.671727i
$274$	2.51939e11	−	4.36371e11i	0.163133	−	0.282555i
$275$	−5.11760e11	−	2.95465e11i	−0.325389	−	0.187863i
$276$	−2.65736e11	+	5.92421e11i	−0.165923	+	0.369901i
$277$	1.17734e12	+	2.03922e12i	0.721945	+	1.25045i	0.960219	+	0.279248i	$0.0900851\pi$
$277$	1.17734e12	+	2.03922e12i	0.721945	+	1.25045i	−0.238274	+	0.971198i	$0.576582\pi$
$278$		−	2.17085e12i		−	1.30739i
$279$	−7.27075e11	−	8.16573e11i	−0.430089	−	0.483030i
$280$	−1.04267e12			−0.605841
$281$	−1.25457e12	+	7.24329e11i	−0.716085	+	0.413432i	−0.813310	−	0.581830i	$-0.802337\pi$
$281$	−1.25457e12	+	7.24329e11i	−0.716085	+	0.413432i	0.0972249	+	0.995262i	$0.469003\pi$
$282$	1.88568e11	+	1.84333e12i	0.105736	+	1.03361i
$283$	1.45881e12	−	2.52673e12i	0.803648	−	1.39196i	−0.113552	−	0.993532i	$-0.536223\pi$
$283$	1.45881e12	−	2.52673e12i	0.803648	−	1.39196i	0.917200	−	0.398427i	$-0.130444\pi$
$284$	1.20792e12	+	6.97390e11i	0.653800	+	0.377472i
$285$	4.03655e12	−	4.12928e11i	2.14677	−	0.219609i
$286$	−6.36962e11	−	1.10325e12i	−0.332877	−	0.576560i
$287$		−	1.24400e11i		−	0.0638868i
$288$	2.61590e11	−	2.32919e11i	0.132026	−	0.117555i
$289$	−1.54413e11			−0.0765942
$290$	−1.32572e11	+	7.65407e10i	−0.0646343	+	0.0373166i
$291$	−1.23304e12	−	5.53091e11i	−0.590896	−	0.265053i
$292$	6.22042e11	−	1.07741e12i	0.293025	−	0.507535i
$293$	1.33675e12	+	7.71772e11i	0.619030	+	0.357397i	0.776491	−	0.630128i	$-0.216998\pi$
$293$	1.33675e12	+	7.71772e11i	0.619030	+	0.357397i	−0.157461	+	0.987525i	$0.550331\pi$
$294$	1.13652e12	+	1.57345e12i	0.517415	+	0.716335i
$295$	1.63968e12	+	2.84000e12i	0.733918	+	1.27118i
$296$		−	1.04969e12i		−	0.461956i
$297$	−2.09807e12	−	1.92100e12i	−0.907901	−	0.831277i
$298$	1.67958e12			0.714691
$299$	1.28348e12	−	7.41017e11i	0.537072	−	0.310079i
$300$	−3.00628e11	+	2.17146e11i	−0.123715	+	0.0893606i
$301$	9.23702e11	−	1.59990e12i	0.373852	−	0.647530i
$302$	8.87931e11	+	5.12647e11i	0.353463	+	0.204072i
$303$	−2.08428e11	+	4.64661e11i	−0.0816101	+	0.181938i
$304$	6.13029e11	+	1.06180e12i	0.236109	+	0.408953i
$305$			2.64244e10i			0.0100116i
$306$	−1.92765e12	+	3.98558e11i	−0.718491	+	0.148554i
$307$	−2.26133e12			−0.829224			−0.414612	−	0.909998i	$-0.636083\pi$
$307$	−2.26133e12			−0.829224			−0.414612	+	0.909998i	$0.636083\pi$
$308$	−2.21598e12	+	1.27939e12i	−0.799487	+	0.461584i
$309$	−3.40988e11	−	3.33330e12i	−0.121045	−	1.18326i
$310$	−7.47907e11	+	1.29541e12i	−0.261240	+	0.452480i
$311$	−1.08915e12	−	6.28821e11i	−0.374357	−	0.216135i	0.301003	−	0.953623i	$-0.402678\pi$
$311$	−1.08915e12	−	6.28821e11i	−0.374357	−	0.216135i	−0.675360	+	0.737488i	$0.736012\pi$
$312$	−7.95327e11	+	8.13600e10i	−0.269013	+	0.0275193i
$313$	1.57235e12	+	2.72340e12i	0.523394	+	0.906545i	0.999629	+	0.0272268i	$0.00866764\pi$
$313$	1.57235e12	+	2.72340e12i	0.523394	+	0.906545i	−0.476236	+	0.879318i	$0.657999\pi$
$314$		−	8.19564e11i		−	0.268494i
$315$	5.04512e12	+	1.67029e12i	1.62674	+	0.538567i
$316$	7.60810e11			0.241457
$317$	−2.20168e12	+	1.27114e12i	−0.687793	+	0.397097i	−0.802785	−	0.596269i	$-0.796649\pi$
$317$	−2.20168e12	+	1.27114e12i	−0.687793	+	0.397097i	0.114992	+	0.993366i	$0.463316\pi$
$318$	4.02816e11	+	1.80687e11i	0.123871	+	0.0555638i
$319$	−1.87836e11	+	3.25341e11i	−0.0568623	+	0.0984885i
$320$	−4.14986e11	−	2.39592e11i	−0.123675	−	0.0714041i
$321$	3.85230e11	+	5.33332e11i	0.113030	+	0.156485i
$322$	−1.48840e12	−	2.57798e12i	−0.429971	−	0.744732i
$323$		−	6.89036e12i		−	1.95988i
$324$	−1.63886e12	+	7.07960e11i	−0.459003	+	0.198282i
$325$	8.46481e11			0.233453
$326$	−2.73853e11	+	1.58109e11i	−0.0743754	+	0.0429407i
$327$	−4.52063e12	+	3.26529e12i	−1.20909	+	0.873339i
$328$	2.85854e10	−	4.95114e10i	0.00752966	−	0.0130417i
$329$	−7.35706e12	−	4.24760e12i	−1.90864	−	1.10196i
$330$	−1.59279e12	+	3.55090e12i	−0.406996	+	0.907338i
$331$	2.79487e12	+	4.84086e12i	0.703432	+	1.21838i	0.967254	+	0.253809i	$0.0816834\pi$
$331$	2.79487e12	+	4.84086e12i	0.703432	+	1.21838i	−0.263822	+	0.964571i	$0.584983\pi$
$332$			3.34906e11i			0.0830295i
$333$	−1.68152e12	+	5.07905e12i	−0.410660	+	1.24040i
$334$	−3.38339e12			−0.813992
$335$	5.90797e12	−	3.41097e12i	1.40028	−	0.808451i
$336$	1.63419e11	+	1.59748e12i	0.0381597	+	0.373027i
$337$	3.41152e12	−	5.90892e12i	0.784871	−	1.35944i	−0.144205	−	0.989548i	$-0.546063\pi$
$337$	3.41152e12	−	5.90892e12i	0.784871	−	1.35944i	0.929076	−	0.369888i	$-0.120604\pi$
$338$	−1.12110e12	−	6.47270e11i	−0.254134	−	0.146724i
$339$	−1.54461e12	+	1.58010e11i	−0.345002	+	0.0352928i
$340$	1.34649e12	+	2.33219e12i	0.296353	+	0.513298i
$341$			3.67082e12i			0.796143i
$342$	−1.26530e12	−	6.11968e12i	−0.270434	−	1.30797i
$343$	−1.77796e12			−0.374499
$344$	7.35269e11	−	4.24508e11i	0.152635	−	0.0881239i
$345$	−4.13098e12	−	1.85299e12i	−0.845197	−	0.379122i
$346$	−1.38837e12	+	2.40473e12i	−0.279979	+	0.484939i
$347$	−2.60540e12	−	1.50423e12i	−0.517877	−	0.298996i	0.218189	−	0.975907i	$-0.429985\pi$
$347$	−2.60540e12	−	1.50423e12i	−0.517877	−	0.298996i	−0.736066	+	0.676910i	$0.763319\pi$
$348$	1.38046e11	+	1.91118e11i	0.0270476	+	0.0374460i
$349$	−1.64881e12	−	2.85583e12i	−0.318452	−	0.551575i	0.661713	−	0.749757i	$-0.269830\pi$
$349$	−1.64881e12	−	2.85583e12i	−0.318452	−	0.551575i	−0.980165	+	0.198182i	$0.936496\pi$
$350$		−	1.70023e12i		−	0.323719i
$351$	3.97863e12	+	8.80389e11i	0.746789	+	0.165249i
$352$	−1.17595e12			−0.217608
$353$	1.04416e12	−	6.02848e11i	0.190500	−	0.109985i	−0.401717	−	0.915764i	$-0.631586\pi$
$353$	1.04416e12	−	6.02848e11i	0.190500	−	0.109985i	0.592217	+	0.805779i	$0.298253\pi$
$354$	4.09418e12	−	2.95726e12i	0.736463	−	0.531954i
$355$	−4.86294e12	+	8.42286e12i	−0.862496	+	1.49389i
$356$	−5.91102e11	−	3.41273e11i	−0.103374	−	0.0596831i
$357$	3.69351e12	−	8.23416e12i	0.636940	−	1.41997i
$358$	3.23491e12	+	5.60303e12i	0.550107	+	0.952814i
$359$			6.75463e12i			1.13274i	0.824152	+	0.566368i	$0.191652\pi$
$359$			6.75463e12i			1.13274i	−0.824152	+	0.566368i	$0.808348\pi$
$360$	1.62416e12	+	1.82408e12i	0.268606	+	0.301669i
$361$	1.57437e13			2.56785
$362$	3.03037e12	−	1.74959e12i	0.487476	−	0.281444i
$363$	3.30524e11	+	3.23101e12i	0.0524408	+	0.512631i
$364$	1.83268e12	−	3.17429e12i	0.286800	−	0.496752i
$365$	7.51282e12	+	4.33753e12i	1.15968	+	0.669543i
$366$	4.04848e10	−	4.14150e9i	0.00616434	−	0.000630597i
$367$	−3.78530e12	−	6.55634e12i	−0.568552	−	0.984762i	−0.996709	−	0.0810572i	$-0.974170\pi$
$367$	−3.78530e12	−	6.55634e12i	−0.568552	−	0.984762i	0.428157	−	0.903704i	$-0.359163\pi$
$368$		−	1.36805e12i		−	0.202705i
$369$	−2.17628e11	+	1.93776e11i	−0.0318114	+	0.0283248i
$370$	7.31952e12			1.05554
$371$	−1.75290e12	+	1.01203e12i	−0.249394	+	0.143988i
$372$	2.10192e12	+	9.42839e11i	0.295055	+	0.132350i
$373$	7.23754e11	−	1.25358e12i	0.100241	−	0.173623i	−0.811543	−	0.584293i	$-0.801372\pi$
$373$	7.23754e11	−	1.25358e12i	0.100241	−	0.173623i	0.911784	+	0.410670i	$0.134705\pi$
$374$	5.72334e12	+	3.30437e12i	0.782153	+	0.451576i
$375$	3.44664e12	+	4.77171e12i	0.464772	+	0.643454i
$376$	−1.95208e12	−	3.38110e12i	−0.259752	−	0.449903i
$377$		−	5.38133e11i		−	0.0706615i
$378$	1.76834e12	−	7.99143e12i	0.229143	−	1.03554i
$379$	−1.17747e13			−1.50576			−0.752878	−	0.658160i	$-0.771335\pi$
$379$	−1.17747e13			−1.50576			−0.752878	+	0.658160i	$0.771335\pi$
$380$	−7.40397e12	+	4.27469e12i	−0.934430	+	0.539493i
$381$	−4.60614e12	+	3.32706e12i	−0.573737	+	0.414415i
$382$	2.24984e12	−	3.89684e12i	0.276589	−	0.479066i
$383$	4.63483e11	+	2.67592e11i	0.0562393	+	0.0324698i	0.527856	−	0.849334i	$-0.322996\pi$
$383$	4.63483e11	+	2.67592e11i	0.0562393	+	0.0324698i	−0.471617	+	0.881804i	$0.656329\pi$
$384$	−3.02039e11	+	6.73352e11i	−0.0361749	+	0.0806466i
$385$	−8.92129e12	−	1.54521e13i	−1.05469	−	1.82677i
$386$			3.31101e12i			0.386388i
$387$	−4.23773e12	+	8.76187e11i	−0.488178	+	0.100935i
$388$	2.84740e12			0.323810
$389$	3.75612e12	−	2.16860e12i	0.421688	−	0.243462i	−0.274111	−	0.961698i	$-0.588384\pi$
$389$	3.75612e12	−	2.16860e12i	0.421688	−	0.243462i	0.695799	+	0.718236i	$0.255050\pi$
$390$	−5.67327e11	−	5.54586e12i	−0.0628797	−	0.614675i
$391$	−3.84418e12	+	6.65831e12i	−0.420649	+	0.728585i
$392$	−3.54174e12	−	2.04482e12i	−0.382636	−	0.220915i
$393$	−1.54533e13	+	1.58083e12i	−1.64838	+	0.168625i
$394$	−1.52372e12	−	2.63916e12i	−0.160481	−	0.277962i
$395$			5.30517e12i			0.551713i
$396$	5.68999e12	+	1.88379e12i	0.584299	+	0.193445i
$397$	−1.37412e13			−1.39339			−0.696694	−	0.717369i	$-0.745346\pi$
$397$	−1.37412e13			−1.39339			−0.696694	+	0.717369i	$0.745346\pi$
$398$	−9.79376e12	+	5.65443e12i	−0.980695	+	0.566204i
$399$	2.61408e13	+	1.17257e13i	2.58497	+	1.15951i
$400$	3.90690e11	−	6.76694e11i	0.0381533	−	0.0660834i
$401$	9.49215e12	+	5.48030e12i	0.915467	+	0.528545i	0.882186	−	0.470901i	$-0.156071\pi$
$401$	9.49215e12	+	5.48030e12i	0.915467	+	0.528545i	0.0332811	+	0.999446i	$0.489404\pi$
$402$	−6.15191e12	−	8.51702e12i	−0.585976	−	0.811255i
$403$	−2.62915e12	−	4.55381e12i	−0.247337	−	0.428401i
$404$		−	1.07302e12i		−	0.0997015i
$405$	−4.93664e12	−	1.14278e13i	−0.453061	−	1.04879i
$406$	−1.08089e12			−0.0979829
$407$	1.55560e13	−	8.98128e12i	1.39292	−	0.804204i
$408$	3.36212e12	−	2.42849e12i	0.297380	−	0.214800i
$409$	−3.08338e12	+	5.34057e12i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$409$	−3.08338e12	+	5.34057e12i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$410$	3.45246e11	+	1.99328e11i	0.0297995	+	0.0172047i
$411$	2.21467e12	−	4.93728e12i	0.188842	−	0.420997i
$412$	3.52995e12	+	6.11405e12i	0.297360	+	0.515042i
$413$			2.31551e13i			1.92706i
$414$	−2.19153e12	+	6.61951e12i	−0.180196	+	0.544282i
$415$	−2.33532e12			−0.189717
$416$	1.45882e12	−	8.42248e11i	0.117094	−	0.0676042i
$417$	−2.37250e12	−	2.31921e13i	−0.188159	−	1.83933i
$418$	−1.04903e13	+	1.81698e13i	−0.822069	+	1.42387i
$419$	−8.91916e12	−	5.14948e12i	−0.690643	−	0.398743i	0.113210	−	0.993571i	$-0.463887\pi$
$419$	−8.91916e12	−	5.14948e12i	−0.690643	−	0.398743i	−0.803853	+	0.594828i	$0.797220\pi$
$420$	−1.11393e13	+	1.13953e12i	−0.852340	+	0.0871923i
$421$	2.00233e12	+	3.46813e12i	0.151400	+	0.262232i	0.931742	−	0.363121i	$-0.118289\pi$
$421$	2.00233e12	+	3.46813e12i	0.151400	+	0.262232i	−0.780343	+	0.625352i	$0.784955\pi$
$422$		−	1.24805e12i		−	0.0932547i
$423$	4.02911e12	+	1.94870e13i	0.297514	+	1.43894i
$424$	−9.30206e11			−0.0678813
$425$	−3.80297e12	+	2.19565e12i	−0.274270	+	0.158350i
$426$	1.36669e13	+	6.13041e12i	0.974138	+	0.436959i
$427$	−9.32894e10	+	1.61582e11i	−0.00657193	+	0.0113829i
$428$	−1.20050e12	−	6.93106e11i	−0.0835875	−	0.0482593i
$429$	−8.01067e12	−	1.10904e13i	−0.551293	−	0.763238i
$430$	2.96012e12	+	5.12707e12i	0.201357	+	0.348760i
$431$		−	6.89382e12i		−	0.463526i	−0.972772	−	0.231763i	$-0.925551\pi$
$431$		−	6.89382e12i		−	0.463526i	0.972772	−	0.231763i	$-0.0744493\pi$
$432$	2.54012e12	−	2.77426e12i	0.168825	−	0.184386i
$433$	1.86892e13			1.22787			0.613934	−	0.789357i	$-0.289586\pi$
$433$	1.86892e13			1.22787			0.613934	+	0.789357i	$0.289586\pi$
$434$	−9.14674e12	+	5.28087e12i	−0.594042	+	0.342971i
$435$	−1.33268e12	+	9.62604e11i	−0.0855616	+	0.0618018i
$436$	5.87491e12	−	1.01756e13i	0.372880	−	0.645847i
$437$	−2.11380e13	−	1.22041e13i	−1.32635	−	0.765768i
$438$	5.46805e12	−	1.21902e13i	0.339205	−	0.756208i
$439$	−7.43204e12	−	1.28727e13i	−0.455812	−	0.789489i	0.542923	−	0.839783i	$-0.317318\pi$
$439$	−7.43204e12	−	1.28727e13i	−0.455812	−	0.789489i	−0.998734	+	0.0502935i	$0.983984\pi$
$440$		−	8.19996e12i		−	0.497219i
$441$	1.38615e13	+	1.55678e13i	0.831031	+	0.933326i
$442$	−9.46675e12			−0.561164
$443$	−7.48917e12	+	4.32387e12i	−0.438950	+	0.253428i	−0.703152	−	0.711039i	$-0.748225\pi$
$443$	−7.48917e12	+	4.32387e12i	−0.438950	+	0.253428i	0.264202	+	0.964467i	$0.414891\pi$
$444$	−1.14719e12	−	1.12142e13i	−0.0664845	−	0.649913i
$445$	2.37971e12	−	4.12178e12i	0.136372	−	0.236203i
$446$	2.40478e12	+	1.38840e12i	0.136270	+	0.0786758i
$447$	1.79436e13	−	1.83559e12i	1.00548	−	0.102858i
$448$	−1.69173e12	−	2.93016e12i	−0.0937434	−	0.162368i
$449$		−	2.13962e13i		−	1.17248i	−0.810137	−	0.586241i	$-0.800607\pi$
$449$		−	2.13962e13i		−	1.17248i	0.810137	−	0.586241i	$-0.199393\pi$
$450$	−2.97442e12	+	2.64842e12i	−0.161191	+	0.143524i
$451$	9.78325e11			0.0524325
$452$	2.83319e12	−	1.63574e12i	0.150170	−	0.0867006i
$453$	1.00464e13	+	4.50642e12i	0.526647	+	0.236233i
$454$	−7.34424e12	+	1.27206e13i	−0.380774	+	0.659520i
$455$	2.21345e13	+	1.27794e13i	1.13504	+	0.655318i
$456$	7.70968e12	+	1.06737e13i	0.391032	+	0.541364i
$457$	8.70254e12	+	1.50732e13i	0.436581	+	0.756181i	0.997423	−	0.0717418i	$-0.0228558\pi$
$457$	8.70254e12	+	1.50732e13i	0.436581	+	0.756181i	−0.560842	+	0.827923i	$0.689522\pi$
$458$			1.42158e13i			0.705413i
$459$	−2.01583e13	+	6.36468e12i	−0.989444	+	0.312401i
$460$	9.53950e12			0.463166
$461$	9.48716e12	−	5.47741e12i	0.455650	−	0.263070i	−0.254563	−	0.967056i	$-0.581932\pi$
$461$	9.48716e12	−	5.47741e12i	0.455650	−	0.263070i	0.710214	+	0.703986i	$0.248598\pi$
$462$	−2.22760e13	+	1.60901e13i	−1.05834	+	0.764451i
$463$	4.36470e12	−	7.55989e12i	0.205140	−	0.355312i	−0.745038	−	0.667023i	$-0.767568\pi$
$463$	4.36470e12	−	7.55989e12i	0.205140	−	0.355312i	0.950177	+	0.311710i	$0.100902\pi$
$464$	−4.30195e11	−	2.48373e11i	−0.0200021	−	0.0115482i
$465$	−6.57447e12	+	1.46568e13i	−0.302410	+	0.674179i
$466$	−6.30503e12	−	1.09206e13i	−0.286918	−	0.496957i
$467$		−	3.61030e13i		−	1.62540i	−0.582685	−	0.812698i	$-0.697998\pi$
$467$		−	3.61030e13i		−	1.62540i	0.582685	−	0.812698i	$-0.302002\pi$
$468$	−8.40790e12	+	1.73841e12i	−0.374506	+	0.0774323i
$469$	4.81688e13			2.12276
$470$	2.35766e13	−	1.36120e13i	1.02800	−	0.593515i
$471$	−8.95691e11	−	8.75575e12i	−0.0386415	−	0.377737i
$472$	−5.32071e12	+	9.21575e12i	−0.227122	+	0.393387i
$473$	1.25822e13	+	7.26431e12i	0.531434	+	0.306824i
$474$	8.12806e12	−	8.31480e11i	0.339700	−	0.0347504i
$475$	−6.97049e12	−	1.20732e13i	−0.288267	−	0.499293i
$476$			1.90148e13i			0.778138i
$477$	4.50093e12	+	1.49013e12i	0.182268	+	0.0603436i
$478$	3.14199e13			1.25912
$479$	9.53550e12	−	5.50532e12i	0.378152	−	0.218326i	−0.298862	−	0.954296i	$-0.596607\pi$
$479$	9.53550e12	−	5.50532e12i	0.378152	−	0.218326i	0.677014	+	0.735970i	$0.263274\pi$
$480$	−4.69532e12	−	2.10613e12i	−0.184272	−	0.0826570i
$481$	−1.28653e13	+	2.22833e13i	−0.499683	+	0.865476i
$482$	−2.11297e13	−	1.21992e13i	−0.812191	−	0.468919i
$483$	−1.87186e13	−	2.59150e13i	−0.712096	−	0.985861i
$484$	−3.42162e12	−	5.92642e12i	−0.128827	−	0.223134i
$485$			1.98551e13i			0.739883i
$486$	−1.67349e13	+	9.35453e12i	−0.617222	+	0.345017i
$487$	−6.44905e11			−0.0235424			−0.0117712	−	0.999931i	$-0.503747\pi$
$487$	−6.44905e11			−0.0235424			−0.0117712	+	0.999931i	$0.503747\pi$
$488$	−7.42587e10	+	4.28733e10i	−0.00268317	+	0.00154913i
$489$	−2.75289e12	+	1.98844e12i	−0.0984567	+	0.0711161i
$490$	1.42587e13	−	2.46967e13i	0.504775	−	0.874296i
$491$	−4.31673e12	−	2.49227e12i	−0.151268	−	0.0873348i	0.422455	−	0.906384i	$-0.361168\pi$
$491$	−4.31673e12	−	2.49227e12i	−0.151268	−	0.0873348i	−0.573724	+	0.819049i	$0.694502\pi$
$492$	2.51280e11	−	5.60192e11i	0.00871630	−	0.0194317i
$493$	1.39584e12	+	2.41766e12i	0.0479292	+	0.0830159i
$494$		−	3.00539e13i		−	1.02157i
$495$	−1.31358e13	+	3.96766e13i	−0.442007	+	1.33508i
$496$	−4.85389e12			−0.161689
$497$	−5.94727e13	+	3.43366e13i	−1.96126	+	1.13234i
$498$	3.66015e11	+	3.57795e12i	0.0119496	+	0.116812i
$499$	−2.13155e13	+	3.69195e13i	−0.688958	+	1.19331i	0.283217	+	0.959056i	$0.408598\pi$
$499$	−2.13155e13	+	3.69195e13i	−0.688958	+	1.19331i	−0.972175	+	0.234255i	$0.924735\pi$
$500$	−1.07408e13	−	6.20121e12i	−0.343706	−	0.198439i
$501$	−3.61463e13	+	3.69767e12i	−1.14518	+	0.117149i
$502$	−1.19176e13	−	2.06419e13i	−0.373826	−	0.647486i
$503$		−	4.31024e13i		−	1.33863i	−0.742978	−	0.669316i	$-0.766587\pi$
$503$		−	4.31024e13i		−	1.33863i	0.742978	−	0.669316i	$-0.233413\pi$
$504$	3.49174e12	+	1.68880e13i	0.107372	+	0.519309i
$505$	7.48224e12			0.227811
$506$	2.02741e13	−	1.17053e13i	0.611209	−	0.352882i
$507$	−1.26846e13	−	5.68982e12i	−0.378650	−	0.169847i
$508$	5.98604e12	−	1.03681e13i	0.176938	−	0.306466i
$509$	−3.11764e13	−	1.79997e13i	−0.912509	−	0.526838i	−0.0312717	−	0.999511i	$-0.509956\pi$
$509$	−3.11764e13	−	1.79997e13i	−0.912509	−	0.526838i	−0.881238	+	0.472673i	$0.843289\pi$
$510$	1.69340e13	+	2.34442e13i	0.490804	+	0.679493i
$511$	3.06267e13	+	5.30470e13i	0.879014	+	1.52250i
$512$		−	1.55494e12i		−	0.0441942i
$513$	−2.02058e13	−	6.39964e13i	−0.568709	−	1.80123i
$514$	−2.42228e12			−0.0675164
$515$	−4.26336e13	+	2.46145e13i	−1.17684	+	0.679446i
$516$	7.39126e12	−	5.33877e12i	0.202055	−	0.145946i
$517$	3.34046e13	−	5.78585e13i	0.904386	−	1.56644i
$518$	4.47580e13	+	2.58411e13i	1.20011	+	0.692886i
$519$	−1.22045e13	+	2.72082e13i	−0.324103	+	0.722541i
$520$	5.87304e12	+	1.01724e13i	0.154471	+	0.267551i
$521$			4.87564e13i			1.27011i	0.772465	+	0.635057i	$0.219023\pi$
$521$			4.87564e13i			1.27011i	−0.772465	+	0.635057i	$0.780977\pi$
$522$	1.68368e12	+	1.89093e12i	0.0434417	+	0.0487891i
$523$	−2.95427e13			−0.754992			−0.377496	−	0.926011i	$-0.623215\pi$
$523$	−2.95427e13			−0.754992			−0.377496	+	0.926011i	$0.623215\pi$
$524$	2.83449e13	−	1.63650e13i	0.717496	−	0.414246i
$525$	−1.85816e12	−	1.81643e13i	−0.0465894	−	0.455430i
$526$	−6.86463e12	+	1.18899e13i	−0.170486	+	0.295290i
$527$	2.36239e13	+	1.36392e13i	0.581163	+	0.335534i
$528$	−1.25632e13	+	1.28518e12i	−0.306147	+	0.0313180i
$529$	−7.09580e12	−	1.22903e13i	−0.171287	−	0.296677i
$530$		−	6.48638e12i		−	0.155104i
$531$	4.05080e13	−	3.60682e13i	0.959551	−	0.854382i
$532$	−6.03660e13			−1.41656
$533$	−1.21366e12	+	7.00704e11i	−0.0282136	+	0.0162892i
$534$	−6.68797e12	−	2.99996e12i	−0.154024	−	0.0690890i
$535$	4.83307e12	−	8.37112e12i	0.110269	−	0.190992i
$536$	1.91713e13	+	1.10685e13i	0.433338	+	0.250188i
$537$	4.06835e13	+	5.63242e13i	0.911059	+	1.26132i
$538$	−2.09907e13	−	3.63569e13i	−0.465709	−	0.806632i
$539$		−	6.99833e13i		−	1.53833i
$540$	1.93451e13	+	1.77124e13i	0.421310	+	0.385752i
$541$	−2.34984e13			−0.507051			−0.253526	−	0.967329i	$-0.581590\pi$
$541$	−2.34984e13			−0.507051			−0.253526	+	0.967329i	$0.581590\pi$
$542$	−1.08944e13	+	6.28988e12i	−0.232920	+	0.134476i
$543$	3.04627e13	−	2.20034e13i	0.645311	−	0.466113i
$544$	−4.36934e12	+	7.56791e12i	−0.0917109	+	0.158848i
$545$	7.09553e13	+	4.09661e13i	1.47572	+	0.852005i
$546$	1.61101e13	−	3.59152e13i	0.331998	−	0.740143i
$547$	1.18795e13	+	2.05759e13i	0.242583	+	0.420167i	0.961449	−	0.274982i	$-0.0886718\pi$
$547$	1.18795e13	+	2.05759e13i	0.242583	+	0.420167i	−0.718866	+	0.695149i	$0.755338\pi$
$548$			1.14015e13i			0.230705i
$549$	4.27991e11	−	8.84907e10i	0.00858168	−	0.00177434i
$550$	1.33712e13			0.265679
$551$	−7.67532e12	+	4.43135e12i	−0.151126	+	0.0872525i
$552$	−1.49513e12	−	1.46155e13i	−0.0291731	−	0.285179i
$553$	−1.87295e13	+	3.24405e13i	−0.362161	+	0.627281i
$554$	−4.61422e13	−	2.66402e13i	−0.884199	−	0.510492i
$555$	7.81975e13	−	7.99941e12i	1.48501	−	0.151912i
$556$	2.45604e13	+	4.25398e13i	0.462233	+	0.800611i
$557$			4.71567e13i			0.879564i	0.898105	+	0.439782i	$0.144944\pi$
$557$			4.71567e13i			0.879564i	−0.898105	+	0.439782i	$0.855056\pi$
$558$	2.34862e13	+	7.77559e12i	0.434152	+	0.143735i
$559$	−2.08116e13			−0.381283
$560$	2.04322e13	−	1.17965e13i	0.371000	−	0.214197i
$561$	6.47563e13	+	2.90471e13i	1.16538	+	0.522743i
$562$	1.63897e13	−	2.83878e13i	0.292341	−	0.506349i
$563$	−6.61521e13	−	3.81929e13i	−1.16950	−	0.675213i	−0.215941	−	0.976406i	$-0.569282\pi$
$563$	−6.61521e13	−	3.81929e13i	−1.16950	−	0.675213i	−0.953563	+	0.301193i	$0.902615\pi$
$564$	−2.45501e13	−	3.39884e13i	−0.430187	−	0.595573i
$565$	1.14061e13	+	1.97560e13i	0.198105	+	0.343128i
$566$			6.60181e13i			1.13653i
$567$	1.01582e13	−	8.73084e13i	0.173341	−	1.48984i
$568$	−3.15603e13			−0.533825
$569$	1.58477e13	−	9.14965e12i	0.265707	−	0.153406i	−0.361228	−	0.932478i	$-0.617642\pi$
$569$	1.58477e13	−	9.14965e12i	0.265707	−	0.153406i	0.626935	+	0.779071i	$0.284309\pi$
$570$	−7.44281e13	+	5.37600e13i	−1.23698	+	0.893480i
$571$	4.54963e13	−	7.88019e13i	0.749542	−	1.29824i	−0.198501	−	0.980101i	$-0.563607\pi$
$571$	4.54963e13	−	7.88019e13i	0.749542	−	1.29824i	0.948043	−	0.318144i	$-0.103059\pi$
$572$	2.49637e13	+	1.44128e13i	0.407689	+	0.235379i
$573$	1.97772e13	−	4.40904e13i	0.320178	−	0.713791i
$574$	1.40743e12	+	2.43773e12i	0.0225874	+	0.0391225i
$575$			1.55555e13i			0.247483i
$576$	−2.49091e12	+	7.52381e12i	−0.0392868	+	0.118666i
$577$	1.70116e13			0.265990			0.132995	−	0.991117i	$-0.457541\pi$
$577$	1.70116e13			0.265990			0.132995	+	0.991117i	$0.457541\pi$
$578$	3.02587e12	−	1.74699e12i	0.0469042	−	0.0270801i
$579$	3.61856e12	+	3.53729e13i	0.0556088	+	0.543599i
$580$	1.73192e12	−	2.99977e12i	0.0263868	−	0.0457034i
$581$	−1.42802e13	−	8.24468e12i	−0.215702	−	0.124536i
$582$	3.04200e13	−	3.11189e12i	0.455559	−	0.0466025i
$583$	−7.95899e12	−	1.37854e13i	−0.118172	−	0.204680i
$584$			2.81504e13i			0.414401i
$585$	−1.21220e13	−	5.86288e13i	−0.176927	−	0.855719i
$586$	−3.49264e13			−0.505436
$587$	2.14336e13	−	1.23747e13i	0.307543	−	0.177560i	−0.338284	−	0.941044i	$-0.609846\pi$
$587$	2.14336e13	−	1.23747e13i	0.307543	−	0.177560i	0.645826	+	0.763484i	$0.276513\pi$
$588$	−4.00726e13	−	1.79750e13i	−0.570114	−	0.255730i
$589$	−4.33003e13	+	7.49983e13i	−0.610822	+	1.05797i
$590$	−6.42619e13	−	3.71016e13i	−0.898863	−	0.518959i
$591$	−1.91629e13	−	2.65300e13i	−0.265780	−	0.367960i
$592$	1.18758e13	+	2.05696e13i	0.163326	+	0.282889i
$593$			4.59854e13i			0.627114i	0.949569	+	0.313557i	$0.101521\pi$
$593$			4.59854e13i			0.627114i	−0.949569	+	0.313557i	$0.898479\pi$
$594$	6.28474e13	+	1.39068e13i	0.849874	+	0.188060i
$595$	−1.32591e14			−1.77799
$596$	−3.29128e13	+	1.90022e13i	−0.437657	+	0.252681i
$597$	−9.84513e13	+	7.11122e13i	−1.29822	+	0.937718i
$598$	−1.67673e13	+	2.90418e13i	−0.219259	+	0.379767i
$599$	6.72024e13	+	3.87993e13i	0.871467	+	0.503142i	0.867835	−	0.496852i	$-0.165511\pi$
$599$	6.72024e13	+	3.87993e13i	0.871467	+	0.503142i	0.00363140	+	0.999993i	$0.498844\pi$
$600$	3.43435e12	−	7.65640e12i	0.0441661	−	0.0984619i
$601$	−1.96449e13	−	3.40260e13i	−0.250540	−	0.433949i	0.713134	−	0.701027i	$-0.247275\pi$
$601$	−1.96449e13	−	3.40260e13i	−0.250540	−	0.433949i	−0.963675	+	0.267079i	$0.913942\pi$
$602$			4.18020e13i			0.528706i
$603$	−7.50317e13	−	8.42676e13i	−0.941148	−	1.05700i
$604$	−2.31998e13			−0.288602
$605$	4.13253e13	−	2.38592e13i	0.509846	−	0.294360i
$606$	−1.17269e12	−	1.14636e13i	−0.0143490	−	0.140267i
$607$	5.62568e12	−	9.74396e12i	0.0682702	−	0.118247i	−0.829870	−	0.557957i	$-0.811585\pi$
$607$	5.62568e12	−	9.74396e12i	0.0682702	−	0.118247i	0.898140	+	0.439710i	$0.144919\pi$
$608$	−2.40257e13	−	1.38713e13i	−0.289174	−	0.166955i
$609$	−1.15476e13	+	1.18129e12i	−0.137849	+	0.0141016i
$610$	−2.98958e11	−	5.17810e11i	−0.00353965	−	0.00613085i
$611$			9.57014e13i			1.12386i
$612$	3.32649e13	−	2.96190e13i	0.387462	−	0.344995i
$613$	−5.33090e12			−0.0615883			−0.0307942	−	0.999526i	$-0.509804\pi$
$613$	−5.33090e12			−0.0615883			−0.0307942	+	0.999526i	$0.509804\pi$
$614$	4.43128e13	−	2.55840e13i	0.507794	−	0.293175i
$615$	3.90625e12	+	1.75219e12i	0.0444001	+	0.0199161i
$616$	2.89494e13	−	5.01418e13i	0.326389	−	0.565323i
$617$	−3.92663e12	−	2.26704e12i	−0.0439131	−	0.0253532i	0.477883	−	0.878424i	$-0.341404\pi$
$617$	−3.92663e12	−	2.26704e12i	−0.0439131	−	0.0253532i	−0.521796	+	0.853070i	$0.674738\pi$
$618$	4.43939e13	+	6.14612e13i	0.492472	+	0.681802i
$619$	−5.70162e13	−	9.87549e13i	−0.627400	−	1.08669i	−0.988071	−	0.153996i	$-0.950786\pi$
$619$	−5.70162e13	−	9.87549e13i	−0.627400	−	1.08669i	0.360671	−	0.932693i	$-0.382548\pi$
$620$		−	3.38464e13i		−	0.369449i
$621$	−1.61786e13	+	7.31141e13i	−0.175180	+	0.791668i
$622$	2.84572e13			0.305661
$623$	2.91034e13	−	1.68028e13i	0.310101	−	0.179037i
$624$	1.46647e13	−	1.05924e13i	0.155006	−	0.111962i
$625$	5.77957e13	−	1.00105e14i	0.606032	−	1.04968i
$626$	−6.16234e13	−	3.55783e13i	−0.641024	−	0.370095i
$627$	−9.22153e13	+	2.05581e14i	−0.951624	+	2.12151i
$628$	9.27231e12	+	1.60601e13i	0.0949270	+	0.164418i
$629$		−	1.33483e14i		−	1.35573i
$630$	−1.17761e14	+	2.43481e13i	−1.18658	+	0.245337i
$631$	1.41815e14			1.41767			0.708837	−	0.705372i	$-0.249220\pi$
$631$	1.41815e14			1.41767			0.708837	+	0.705372i	$0.249220\pi$
$632$	−1.49088e13	+	8.60758e12i	−0.147862	+	0.0853681i
$633$	−1.36398e12	−	1.33335e13i	−0.0134212	−	0.131197i
$634$	2.87626e13	−	4.98183e13i	0.280790	−	0.486343i
$635$	7.22975e13	+	4.17410e13i	0.700253	+	0.404291i
$636$	−9.93779e12	+	1.01661e12i	−0.0955002	+	0.00976943i
$637$	5.01240e13	+	8.68173e13i	0.477913	+	0.827769i
$638$		−	8.50047e12i		−	0.0804155i
$639$	1.52709e14	+	5.05574e13i	1.43337	+	0.474548i
$640$	1.08427e13			0.100981
$641$	−7.60797e13	+	4.39246e13i	−0.703037	+	0.405899i	−0.808478	−	0.588527i	$-0.799708\pi$
$641$	−7.60797e13	+	4.39246e13i	−0.703037	+	0.405899i	0.105440	+	0.994426i	$0.466375\pi$
$642$	−1.35829e13	−	6.09274e12i	−0.124542	−	0.0558647i
$643$	4.53021e13	−	7.84656e13i	0.412158	−	0.713878i	−0.582968	−	0.812495i	$-0.698109\pi$
$643$	4.53021e13	−	7.84656e13i	0.412158	−	0.713878i	0.995125	+	0.0986170i	$0.0314419\pi$
$644$	5.83330e13	+	3.36786e13i	0.526605	+	0.304036i
$645$	3.72275e13	+	5.15396e13i	0.333477	+	0.461682i
$646$	7.79555e13	+	1.35023e14i	0.692922	+	1.20018i
$647$		−	9.79400e12i		−	0.0863851i	−0.999067	−	0.0431925i	$-0.986247\pi$
$647$		−	9.79400e12i		−	0.0863851i	0.999067	−	0.0431925i	$-0.0137529\pi$
$648$	2.41052e13	−	3.24147e13i	0.210978	−	0.283705i
$649$	−1.82099e14			−1.58156
$650$	−1.65876e13	+	9.57684e12i	−0.142960	+	0.0825383i
$651$	−9.19471e13	+	6.64142e13i	−0.786381	+	0.568010i
$652$	3.57760e12	−	6.19659e12i	0.0303636	−	0.0525914i
$653$	−2.99159e13	−	1.72720e13i	−0.251963	−	0.145471i	0.368700	−	0.929548i	$-0.379803\pi$
$653$	−2.99159e13	−	1.72720e13i	−0.251963	−	0.145471i	−0.620663	+	0.784078i	$0.713136\pi$
$654$	5.16434e13	−	1.15131e14i	0.431644	−	0.962288i
$655$	1.14114e14	+	1.97651e14i	0.946524	+	1.63943i
$656$			1.29363e12i			0.0106485i
$657$	4.50950e13	−	1.36209e14i	0.368385	−	1.11271i
$658$	1.92225e14			1.55840
$659$	−3.63603e13	+	2.09926e13i	−0.292550	+	0.168904i	−0.639091	−	0.769131i	$-0.720689\pi$
$659$	−3.63603e13	+	2.09926e13i	−0.292550	+	0.168904i	0.346541	+	0.938035i	$0.387356\pi$
$660$	−8.96163e12	−	8.76036e13i	−0.0715595	−	0.699524i
$661$	4.07961e13	−	7.06609e13i	0.323304	−	0.559979i	−0.657863	−	0.753137i	$-0.728540\pi$
$661$	4.07961e13	−	7.06609e13i	0.323304	−	0.559979i	0.981168	+	0.193158i	$0.0618729\pi$
$662$	−1.09536e14	−	6.32408e13i	−0.861525	−	0.497402i
$663$	−1.01137e14	+	1.03461e13i	−0.789485	+	0.0807623i
$664$	−3.78903e12	−	6.56279e12i	−0.0293554	−	0.0508450i
$665$		−	4.20935e14i		−	3.23673i
$666$	−2.45118e13	−	1.18553e14i	−0.187070	−	0.904776i
$667$	9.88912e12			0.0749080
$668$	6.63007e13	−	3.82787e13i	0.498466	−	0.287790i
$669$	2.72087e13	+	1.22047e13i	0.203038	+	0.0910748i
$670$	−7.71814e13	+	1.33682e14i	−0.571661	+	0.990147i
$671$	−1.27074e12	−	7.33661e11i	−0.00934207	−	0.00539365i
$672$	−2.12758e13	−	2.94553e13i	−0.155253	−	0.214940i
$673$	4.90463e13	+	8.49506e13i	0.355247	+	0.615306i	0.987160	−	0.159733i	$-0.0510634\pi$
$673$	4.90463e13	+	8.49506e13i	0.355247	+	0.615306i	−0.631913	+	0.775039i	$0.717730\pi$
$674$			1.54388e14i			1.10997i
$675$	−2.88826e13	+	3.15449e13i	−0.206119	+	0.225118i
$676$	2.92921e13			0.207499
$677$	1.66206e14	−	9.59590e13i	1.16870	−	0.674750i	0.215327	−	0.976542i	$-0.430918\pi$
$677$	1.66206e14	−	9.59590e13i	1.16870	−	0.674750i	0.953374	+	0.301793i	$0.0975850\pi$
$678$	2.84805e13	−	2.05717e13i	0.198792	−	0.143589i
$679$	−7.00970e13	+	1.21412e14i	−0.485681	+	0.841223i
$680$	−5.27715e13	−	3.04676e13i	−0.362956	−	0.209553i
$681$	−6.45595e13	+	1.43926e14i	−0.440783	+	0.982661i
$682$	−4.15306e13	−	7.19331e13i	−0.281479	−	0.487536i
$683$			6.12781e13i			0.412289i	0.978522	+	0.206145i	$0.0660917\pi$
$683$			6.12781e13i			0.412289i	−0.978522	+	0.206145i	$0.933908\pi$
$684$	9.40310e13	+	1.05606e14i	0.628044	+	0.705353i
$685$	−7.95030e13			−0.527146
$686$	3.48407e13	−	2.01153e13i	0.229333	−	0.132405i
$687$	1.55363e13	+	1.51873e14i	0.101523	+	0.992426i
$688$	−9.60552e12	+	1.66372e13i	−0.0623130	+	0.107929i
$689$	1.97470e13	+	1.14009e13i	0.127176	+	0.0734249i
$690$	1.01915e14	−	1.04256e13i	0.651615	−	0.0666586i
$691$	−1.26361e14	−	2.18864e14i	−0.802089	−	1.38926i	−0.918239	−	0.396028i	$-0.870388\pi$
$691$	−1.26361e14	−	2.18864e14i	−0.802089	−	1.38926i	0.116149	−	0.993232i	$-0.462945\pi$
$692$		−	6.28307e13i		−	0.395951i
$693$	−2.20399e14	+	1.96243e14i	−1.37894	+	1.22780i
$694$	6.80736e13			0.422845
$695$	−2.96632e14	+	1.71261e14i	−1.82934	+	1.05617i
$696$	−4.86740e12	−	2.18332e12i	−0.0298024	−	0.0133682i
$697$	3.63505e12	−	6.29609e12i	0.0220977	−	0.0382743i
$698$	6.46200e13	+	3.73084e13i	0.390022	+	0.225180i
$699$	−7.92944e13	−	1.09779e14i	−0.475178	−	0.657861i
$700$	1.92359e13	+	3.33176e13i	0.114452	+	0.198236i
$701$		−	1.32926e14i		−	0.785271i	−0.919694	−	0.392636i	$-0.871563\pi$
$701$		−	1.32926e14i		−	0.785271i	0.919694	−	0.392636i	$-0.128437\pi$
$702$	−8.79254e13	+	2.77610e13i	−0.515737	+	0.162836i
$703$	4.23766e14			2.46802
$704$	2.30438e13	−	1.33043e13i	0.133257	−	0.0769361i
$705$	2.37003e14	−	1.71189e14i	1.36084	−	0.982948i
$706$	−1.36409e13	+	2.36267e13i	−0.0777712	+	0.134704i
$707$	4.57531e13	+	2.64155e13i	0.259014	+	0.149542i
$708$	−4.67717e13	+	1.04271e14i	−0.262916	+	0.586133i
$709$	−1.07480e13	−	1.86161e13i	−0.0599924	−	0.103910i	0.834469	−	0.551054i	$-0.185774\pi$
$709$	−1.07480e13	−	1.86161e13i	−0.0599924	−	0.103910i	−0.894462	+	0.447144i	$0.852441\pi$
$710$		−	2.20072e14i		−	1.21975i
$711$	8.59268e13	−	1.77661e13i	0.472912	−	0.0977787i
$712$	1.54442e13			0.0844047
$713$	8.36841e13	−	4.83151e13i	0.454146	−	0.262201i
$714$	2.07810e13	+	2.03143e14i	0.111989	+	1.09474i
$715$	−1.00501e14	+	1.74073e14i	−0.537826	+	0.931541i
$716$	−1.26782e14	−	7.31977e13i	−0.673741	−	0.388985i
$717$	3.35673e14	−	3.43385e13i	1.77141	−	0.181211i
$718$	−7.64199e13	−	1.32363e14i	−0.400483	−	0.693657i
$719$			2.35028e14i			1.22314i	0.791191	+	0.611569i	$0.209461\pi$
$719$			2.35028e14i			1.22314i	−0.791191	+	0.611569i	$0.790539\pi$
$720$	−5.24639e13	−	1.73693e13i	−0.271143	−	0.0897675i
$721$	−3.47600e14			−1.78403
$722$	−3.08511e14	+	1.78119e14i	−1.57248	+	0.907872i
$723$	−2.39070e14	−	1.07237e14i	−1.21014	−	0.542819i
$724$	−3.95886e13	+	6.85695e13i	−0.199011	+	0.344697i
$725$	4.89156e12	+	2.82414e12i	0.0244206	+	0.0140993i
$726$	−4.30316e13	−	5.95751e13i	−0.213356	−	0.295380i
$727$	−9.26722e13	−	1.60513e14i	−0.456328	−	0.790384i	0.542435	−	0.840098i	$-0.317502\pi$
$727$	−9.26722e13	−	1.60513e14i	−0.456328	−	0.790384i	−0.998764	+	0.0497138i	$0.984169\pi$
$728$			8.29375e13i			0.405596i
$729$	−1.68563e14	+	1.18228e14i	−0.818698	+	0.574225i
$730$	−1.96294e14			−0.946876
$731$	9.35001e13	−	5.39823e13i	0.447945	−	0.258621i
$732$	−7.46482e11	+	5.39190e11i	−0.00355192	+	0.00256558i
$733$	3.96953e13	−	6.87543e13i	0.187594	−	0.324922i	−0.756854	−	0.653585i	$-0.773264\pi$
$733$	3.96953e13	−	6.87543e13i	0.187594	−	0.324922i	0.944448	+	0.328662i	$0.106598\pi$
$734$	1.48353e14	+	8.56517e13i	0.696332	+	0.402027i
$735$	1.25341e14	−	2.79429e14i	0.584326	−	1.30267i
$736$	1.54777e13	+	2.68082e13i	0.0716669	+	0.124131i
$737$			3.78816e14i			1.74217i
$738$	2.07230e12	−	6.25939e12i	0.00946611	−	0.0285924i
$739$	−1.27528e13			−0.0578607			−0.0289303	−	0.999581i	$-0.509210\pi$
$739$	−1.27528e13			−0.0578607			−0.0289303	+	0.999581i	$0.509210\pi$
$740$	−1.43433e14	+	8.28109e13i	−0.646382	+	0.373189i
$741$	−3.28456e13	−	3.21079e14i	−0.147023	−	1.43721i
$742$	2.28997e13	−	3.96635e13i	0.101815	−	0.176348i
$743$	3.68802e13	+	2.12928e13i	0.162873	+	0.0940349i	0.579221	−	0.815171i	$-0.303357\pi$
$743$	3.68802e13	+	2.12928e13i	0.162873	+	0.0940349i	−0.416348	+	0.909205i	$0.636690\pi$
$744$	−5.18561e13	+	5.30475e12i	−0.227476	+	0.0232702i
$745$	−1.32504e14	−	2.29503e14i	−0.577359	−	1.00002i
$746$			3.27534e13i			0.141763i
$747$	7.82059e12	+	3.78247e13i	0.0336230	+	0.162620i
$748$	−1.49539e14			−0.638625
$749$	5.91073e13	−	3.41256e13i	0.250745	−	0.144768i
$750$	−1.21526e14	−	5.45117e13i	−0.512109	−	0.229712i
$751$	1.66568e13	−	2.88504e13i	0.0697255	−	0.120768i	−0.829055	−	0.559167i	$-0.811121\pi$
$751$	1.66568e13	−	2.88504e13i	0.0697255	−	0.120768i	0.898780	+	0.438399i	$0.144454\pi$
$752$	7.65057e13	+	4.41706e13i	0.318130	+	0.183672i
$753$	−1.49880e14	−	2.07501e14i	−0.619111	−	0.857129i
$754$	6.08828e12	+	1.05452e13i	0.0249826	+	0.0432712i
$755$		−	1.61773e14i		−	0.659435i
$756$	5.57605e13	+	1.76606e14i	0.225797	+	0.715148i
$757$	2.84299e14			1.14366			0.571829	−	0.820373i	$-0.306234\pi$
$757$	2.84299e14			1.14366			0.571829	+	0.820373i	$0.306234\pi$
$758$	2.30737e14	−	1.33216e14i	0.922084	−	0.532365i
$759$	2.03805e14	−	1.47210e14i	0.809106	−	0.584424i
$760$	9.67251e13	−	1.67533e14i	0.381479	−	0.660742i
$761$	−4.08731e13	−	2.35981e13i	−0.160145	−	0.0924600i	0.417786	−	0.908546i	$-0.362806\pi$
$761$	−4.08731e13	−	2.35981e13i	−0.160145	−	0.0924600i	−0.577931	+	0.816086i	$0.696140\pi$
$762$	5.26203e13	−	1.17309e14i	0.204823	−	0.456623i
$763$	2.89256e14	+	5.01006e14i	1.11856	+	1.93740i
$764$			1.01816e14i			0.391156i
$765$	2.06535e14	+	2.31958e14i	0.788290	+	0.885324i
$766$	−1.21098e13			−0.0459192
$767$	2.25902e14	−	1.30425e14i	0.851028	−	0.491341i
$768$	−1.69938e12	−	1.66121e13i	−0.00636040	−	0.0621755i
$769$	−8.80614e13	+	1.52527e14i	−0.327457	+	0.567172i	−0.982006	−	0.188847i	$-0.939525\pi$
$769$	−8.80614e13	+	1.52527e14i	−0.327457	+	0.567172i	0.654550	+	0.756019i	$0.272858\pi$
$770$	3.49642e14	+	2.01866e14i	1.29172	+	0.745777i
$771$	−2.58783e13	+	2.64728e12i	−0.0949869	+	0.00971692i
$772$	−3.74598e13	−	6.48823e13i	−0.136609	−	0.236614i
$773$			4.29604e14i			1.55658i	0.627906	+	0.778289i	$0.283912\pi$
$773$			4.29604e14i			1.55658i	−0.627906	+	0.778289i	$0.716088\pi$
$774$	7.31293e13	−	6.51141e13i	0.263261	−	0.234407i
$775$	5.51914e13			0.197407
$776$	−5.57974e13	+	3.22147e13i	−0.198292	+	0.114484i
$777$	5.06411e14	+	2.27156e14i	1.78812	+	0.802081i
$778$	−4.90698e13	+	8.49913e13i	−0.172154	+	0.298179i
$779$	1.99881e13	+	1.15401e13i	0.0696761	+	0.0402275i
$780$	7.38615e13	+	1.02258e14i	0.255826	+	0.354179i
$781$	−2.70035e14	−	4.67714e14i	−0.929318	−	1.60963i
$782$		−	1.73968e14i		−	0.594887i
$783$	2.00540e13	+	1.83615e13i	0.0681386	+	0.0623879i
$784$	9.25381e13			0.312421
$785$	−1.11988e14	+	6.46563e13i	−0.375684	+	0.216901i
$786$	2.84936e14	−	2.05812e14i	0.949806	−	0.686053i
$787$	4.99579e13	−	8.65296e13i	0.165474	−	0.286610i	−0.771349	−	0.636412i	$-0.780418\pi$
$787$	4.99579e13	−	8.65296e13i	0.165474	−	0.286610i	0.936824	+	0.349802i	$0.113751\pi$
$788$	5.97174e13	+	3.44779e13i	0.196549	+	0.113477i
$789$	−6.03435e13	+	1.34527e14i	−0.197354	+	0.439971i
$790$	−6.00211e13	−	1.03960e14i	−0.195060	−	0.337854i
$791$			1.61074e14i			0.520167i
$792$	−1.32813e14	+	2.74603e13i	−0.426202	+	0.0881209i
$793$	2.10187e12			0.00670256
$794$	2.69271e14	−	1.55464e14i	0.853272	−	0.492637i
$795$	−7.08888e12	−	6.92968e13i	−0.0223225	−	0.218211i
$796$	1.27945e14	−	2.21607e14i	0.400367	−	0.693456i
$797$	−1.57786e14	−	9.10975e13i	−0.490654	−	0.283279i	0.234192	−	0.972190i	$-0.424756\pi$
$797$	−1.57786e14	−	9.10975e13i	−0.490654	−	0.283279i	−0.724846	+	0.688911i	$0.758089\pi$
$798$	−6.44916e14	+	6.59732e13i	−1.99291	+	0.203870i
$799$	−2.48235e14	−	4.29956e14i	−0.762307	−	1.32035i
$800$			1.76806e13i			0.0539569i
$801$	−7.47291e13	−	2.47406e13i	−0.226635	−	0.0750323i
$802$	−2.48010e14			−0.747476
$803$	−4.17180e14	+	2.40859e14i	−1.24953	+	0.721416i
$804$	2.16911e14	+	9.72978e13i	0.645658	+	0.289616i
$805$	−2.34843e14	+	4.06759e14i	−0.694700	+	1.20326i
$806$	1.03041e14	+	5.94908e13i	0.302925	+	0.174894i
$807$	−2.63986e14	−	3.65476e14i	−0.771283	−	1.06780i
$808$	1.21399e13	+	2.10268e13i	0.0352498	+	0.0610545i
$809$		−	5.53322e14i		−	1.59674i	−0.602164	−	0.798372i	$-0.705695\pi$
$809$		−	5.53322e14i		−	1.59674i	0.602164	−	0.798372i	$-0.294305\pi$
$810$	2.26029e14	+	1.68087e14i	0.648246	+	0.482069i
$811$	3.72399e14			1.06146			0.530731	−	0.847540i	$-0.321917\pi$
$811$	3.72399e14			1.06146			0.530731	+	0.847540i	$0.321917\pi$
$812$	2.11810e13	−	1.22288e13i	0.0600020	−	0.0346422i
$813$	−1.09515e14	+	7.91039e13i	−0.308335	+	0.222713i
$814$	−2.03223e14	+	3.51993e14i	−0.568658	+	0.984944i
$815$	4.32091e13	+	2.49468e13i	0.120168	+	0.0693788i
$816$	−3.84086e13	+	8.56265e13i	−0.106164	+	0.236678i
$817$	1.71377e14	+	2.96833e14i	0.470806	+	0.815459i
$818$		−	1.39538e14i		−	0.381000i
$819$	1.32860e14	−	4.01304e14i	0.360558	−	1.08907i
$820$	−9.02054e12			−0.0243312
$821$	−1.68216e14	+	9.71198e13i	−0.450975	+	0.260370i	−0.708242	−	0.705970i	$-0.750511\pi$
$821$	−1.68216e14	+	9.71198e13i	−0.450975	+	0.260370i	0.257267	+	0.966340i	$0.417178\pi$
$822$	1.24605e13	+	1.21807e14i	0.0332030	+	0.324573i
$823$	−2.13293e14	+	3.69434e14i	−0.564907	+	0.978448i	0.432151	+	0.901801i	$0.357755\pi$
$823$	−2.13293e14	+	3.69434e14i	−0.564907	+	0.978448i	−0.997058	+	0.0766469i	$0.975579\pi$
$824$	−1.38345e14	−	7.98736e13i	−0.364190	−	0.210265i
$825$	1.42850e14	−	1.46132e13i	0.373776	−	0.0382364i
$826$	−2.61970e14	−	4.53745e14i	−0.681319	−	1.18008i
$827$			3.08388e14i			0.797206i	0.917124	+	0.398603i	$0.130505\pi$
$827$			3.08388e14i			0.797206i	−0.917124	+	0.398603i	$0.869495\pi$
$828$	−3.19462e13	−	1.54510e14i	−0.0820857	−	0.397012i
$829$	−1.19874e14			−0.306162			−0.153081	−	0.988214i	$-0.548920\pi$
$829$	−1.19874e14			−0.306162			−0.153081	+	0.988214i	$0.548920\pi$
$830$	4.57627e13	−	2.64211e13i	0.116177	−	0.0670750i
$831$	−5.22072e14	−	2.34181e14i	−1.31742	−	0.590944i
$832$	−1.90579e13	+	3.30093e13i	−0.0478034	+	0.0827979i
$833$	−4.50383e14	−	2.60029e14i	−1.12294	−	0.648330i
$834$	3.08880e14	+	4.27629e14i	0.765526	+	1.05983i
$835$	2.66920e14	+	4.62318e14i	0.657579	+	1.13896i
$836$		−	4.74739e14i		−	1.16258i
$837$	2.59411e14	+	5.74022e13i	0.631482	+	0.139734i
$838$	2.33039e14			0.563908
$839$	−4.70910e14	+	2.71880e14i	−1.13273	+	0.653984i	−0.944621	−	0.328163i	$-0.893570\pi$
$839$	−4.70910e14	+	2.71880e14i	−1.13273	+	0.653984i	−0.188113	+	0.982147i	$0.560237\pi$
$840$	2.05393e14	−	1.48357e14i	0.491123	−	0.354742i
$841$	−2.08558e14	+	3.61233e14i	−0.495732	+	0.858634i
$842$	−7.84749e13	−	4.53075e13i	−0.185426	−	0.107056i
$843$	1.44073e14	−	3.21191e14i	0.338412	−	0.754441i
$844$	1.41201e13	+	2.44567e13i	0.0329705	+	0.0571066i
$845$			2.04255e14i			0.474121i
$846$	−2.99425e14	−	3.36282e14i	−0.690933	−	0.775982i
$847$	3.36933e14			0.772905
$848$	1.82282e13	−	1.05241e13i	0.0415686	−	0.0239997i
$849$	7.21504e13	+	7.05300e14i	0.163569	+	1.59895i
$850$	4.96818e13	−	8.60515e13i	0.111970	−	0.193938i
$851$	−4.09494e14	−	2.36422e14i	−0.917488	−	0.529712i
$852$	−3.37172e14	+	3.44919e13i	−0.751024	+	0.0768278i
$853$	8.41982e13	+	1.45835e14i	0.186448	+	0.322937i	0.944063	−	0.329764i	$-0.106969\pi$
$853$	8.41982e13	+	1.45835e14i	0.186448	+	0.322937i	−0.757616	+	0.652701i	$0.773636\pi$
$854$		−	4.22180e12i		−	0.00929412i
$855$	−7.36393e14	+	6.55683e14i	−1.61168	+	1.43504i
$856$	3.13664e13			0.0682489
$857$	6.47931e14	−	3.74083e14i	1.40160	−	0.809215i	0.407045	−	0.913408i	$-0.366559\pi$
$857$	6.47931e14	−	3.74083e14i	1.40160	−	0.809215i	0.994557	+	0.104193i	$0.0332259\pi$
$858$	2.82450e14	+	1.26696e14i	0.607442	+	0.272474i
$859$	3.18902e14	−	5.52355e14i	0.681854	−	1.18101i	−0.292560	−	0.956247i	$-0.594507\pi$
$859$	3.18902e14	−	5.52355e14i	0.681854	−	1.18101i	0.974414	−	0.224759i	$-0.0721595\pi$
$860$	−1.16012e14	−	6.69798e13i	−0.246611	−	0.142381i
$861$	1.77003e13	+	2.45052e13i	0.0374080	+	0.0517896i
$862$	7.79947e13	+	1.35091e14i	0.163881	+	0.283850i
$863$		−	3.63404e14i		−	0.759163i	−0.925158	−	0.379582i	$-0.876068\pi$
$863$		−	3.63404e14i		−	0.759163i	0.925158	−	0.379582i	$-0.123932\pi$
$864$	−1.83888e13	+	8.31024e13i	−0.0381931	+	0.172602i
$865$	4.38121e14			0.904720
$866$	−3.66232e14	+	2.11444e14i	−0.751912	+	0.434117i
$867$	3.04174e13	−	2.19708e13i	0.0620908	−	0.0448487i
$868$	1.19492e14	−	2.06967e14i	0.242517	−	0.420051i
$869$	−2.55123e14	−	1.47296e14i	−0.514815	−	0.297229i
$870$	1.52244e13	−	3.39406e13i	0.0305453	−	0.0680963i
$871$	−2.71319e14	−	4.69938e14i	−0.541239	−	0.937454i
$872$			2.65868e14i			0.527332i
$873$	3.21589e14	−	6.64913e13i	0.634206	−	0.131127i
$874$	5.52292e14			1.08296
$875$	5.28832e14	−	3.05321e14i	1.03105	−	0.595274i
$876$	3.07652e13	+	3.00743e14i	0.0596403	+	0.583008i
$877$	−1.90373e14	+	3.29736e14i	−0.366951	+	0.635577i	−0.989087	−	0.147332i	$-0.952932\pi$
$877$	−1.90373e14	+	3.29736e14i	−0.366951	+	0.635577i	0.622136	+	0.782909i	$0.286265\pi$
$878$	2.91275e14	+	1.68168e14i	0.558253	+	0.322308i
$879$	−3.73134e14	+	3.81707e13i	−0.711083	+	0.0727420i
$880$	9.27719e13	+	1.60686e14i	0.175794	+	0.304483i
$881$		−	2.25379e14i		−	0.424654i	−0.977199	−	0.212327i	$-0.931896\pi$
$881$		−	2.25379e14i		−	0.424654i	0.977199	−	0.212327i	$-0.0681041\pi$
$882$	−4.47758e14	−	1.48240e14i	−0.838881	−	0.277729i
$883$	−1.39909e14			−0.260640			−0.130320	−	0.991472i	$-0.541600\pi$
$883$	−1.39909e14			−0.260640			−0.130320	+	0.991472i	$0.541600\pi$
$884$	1.85510e14	−	1.07104e14i	0.343641	−	0.198401i
$885$	−7.27085e14	−	3.26141e14i	−1.33927	−	0.600744i
$886$	9.78381e13	−	1.69461e14i	0.179201	−	0.310385i
$887$	3.53460e14	+	2.04070e14i	0.643758	+	0.371674i	0.786061	−	0.618149i	$-0.212117\pi$
$887$	3.53460e14	+	2.04070e14i	0.643758	+	0.371674i	−0.142303	+	0.989823i	$0.545451\pi$
$888$	1.49355e14	+	2.06774e14i	0.270492	+	0.374483i
$889$	2.94728e14	+	5.10483e14i	0.530777	+	0.919333i
$890$			1.07694e14i			0.192859i
$891$	6.86624e14	+	7.98874e13i	1.22273	+	0.142262i
$892$	−6.28319e13			−0.111264
$893$	1.36498e15	−	7.88069e14i	2.40363	−	1.38774i
$894$	−3.30855e14	+	2.38979e14i	−0.579361	+	0.418478i
$895$	5.10412e14	−	8.84059e14i	0.888803	−	1.53945i
$896$	6.63020e13	+	3.82795e13i	0.114812	+	0.0662866i
$897$	−1.47393e14	+	3.28591e14i	−0.253813	+	0.565840i
$898$	2.42071e14	+	4.19279e14i	0.414535	+	0.717995i
$899$		−	3.50868e13i		−	0.0597511i
$900$	2.83231e13	−	8.55499e13i	0.0479654	−	0.144880i
$901$	−1.18289e14			−0.199215
$902$	−1.91712e13	+	1.10685e13i	−0.0321082	+	0.0185377i
$903$	4.56849e13	+	4.46588e14i	0.0760910	+	0.743821i
$904$	−3.70126e13	+	6.41077e13i	−0.0613066	+	0.106186i
$905$	−4.78139e14	−	2.76053e14i	−0.787610	−	0.454727i
$906$	−2.47853e14	+	2.53547e13i	−0.406025	+	0.0415354i
$907$	1.18670e14	+	2.05542e14i	0.193332	+	0.334861i	0.946352	−	0.323136i	$-0.104737\pi$
$907$	1.18670e14	+	2.05542e14i	0.193332	+	0.334861i	−0.753021	+	0.657997i	$0.771404\pi$
$908$		−	3.32362e14i		−	0.538496i
$909$	−2.50568e13	−	1.21188e14i	−0.0403743	−	0.195273i
$910$	−5.78328e14			−0.926760
$911$	−2.88814e14	+	1.66747e14i	−0.460284	+	0.265745i	−0.712164	−	0.702013i	$-0.752285\pi$
$911$	−2.88814e14	+	1.66747e14i	−0.460284	+	0.265745i	0.251880	+	0.967759i	$0.418951\pi$
$912$	−2.71837e14	−	1.21935e14i	−0.430858	−	0.193266i
$913$	6.48390e13	−	1.12305e14i	0.102207	−	0.177029i
$914$	−3.41069e14	−	1.96916e14i	−0.534701	−	0.308710i
$915$	−3.75980e12	−	5.20526e12i	−0.00586218	−	0.00811590i
$916$	−1.60833e14	−	2.78571e14i	−0.249401	−	0.431976i
$917$			1.61148e15i			2.48530i
$918$	3.23013e14	−	3.52787e14i	0.495458	−	0.541127i
$919$	−5.90087e14			−0.900199			−0.450100	−	0.892978i	$-0.648611\pi$
$919$	−5.90087e14			−0.900199			−0.450100	+	0.892978i	$0.648611\pi$
$920$	−1.86935e14	+	1.07927e14i	−0.283630	+	0.163754i
$921$	4.45452e14	−	3.21754e14i	0.672207	−	0.485541i
$922$	−1.23940e14	+	2.14670e14i	−0.186018	+	0.322193i
$923$	6.69980e14	+	3.86813e14i	1.00012	+	0.577421i
$924$	2.54479e14	−	5.67325e14i	0.377827	−	0.842310i
$925$	−1.35035e14	−	2.33888e14i	−0.199406	−	0.345381i
$926$			1.97524e14i			0.290111i
$927$	5.41450e14	+	6.08099e14i	0.790969	+	0.888332i
$928$	1.12401e13			0.0163316
$929$	2.04348e14	−	1.17980e14i	0.295319	−	0.170503i	−0.345019	−	0.938596i	$-0.612128\pi$
$929$	2.04348e14	−	1.17980e14i	0.295319	−	0.170503i	0.640338	+	0.768093i	$0.278794\pi$
$930$	−3.69903e13	−	3.61596e14i	−0.0531708	−	0.519767i
$931$	8.25509e14	−	1.42982e15i	1.18025	−	2.04425i
$932$	2.47106e14	+	1.42667e14i	0.351401	+	0.202882i
$933$	3.04020e14	−	3.11005e13i	0.430026	−	0.0439905i
$934$	4.08459e14	+	7.07472e14i	0.574664	+	0.995348i
$935$		−	1.04274e15i		−	1.45921i
$936$	1.45093e14	−	1.29190e14i	0.201961	−	0.179825i
$937$	3.09488e14			0.428494			0.214247	−	0.976779i	$-0.431270\pi$
$937$	3.09488e14			0.428494			0.214247	+	0.976779i	$0.431270\pi$
$938$	−9.43912e14	+	5.44968e14i	−1.29992	+	0.750510i
$939$	−6.97233e14	−	3.12751e14i	−0.955102	−	0.428421i
$940$	−3.08004e14	+	5.33478e14i	−0.419678	+	0.726904i
$941$	−3.49495e14	−	2.01781e14i	−0.473689	−	0.273484i	0.244094	−	0.969752i	$-0.421509\pi$
$941$	−3.49495e14	−	2.01781e14i	−0.473689	−	0.273484i	−0.717783	+	0.696267i	$0.754843\pi$
$942$	1.16612e14	+	1.61443e14i	0.157213	+	0.217654i
$943$	−1.28766e13	−	2.23030e13i	−0.0172681	−	0.0299092i
$944$		−	2.40788e14i		−	0.321199i
$945$	−1.23148e15	+	3.88821e14i	−1.63406	+	0.515930i
$946$	−3.28745e14			−0.433914
$947$	−1.19158e15	+	6.87961e14i	−1.56450	+	0.903263i	−0.567705	+	0.823232i	$0.692169\pi$
$947$	−1.19158e15	+	6.87961e14i	−1.56450	+	0.903263i	−0.996792	+	0.0800310i	$0.974498\pi$
$948$	−1.49870e14	+	1.08252e14i	−0.195737	+	0.141382i
$949$	3.45020e14	−	5.97593e14i	0.448243	−	0.776380i
$950$	2.73186e14	+	1.57724e14i	0.353054	+	0.203836i
$951$	2.52837e14	−	5.63665e14i	0.325042	−	0.724633i
$952$	−2.15128e14	−	3.72612e14i	−0.275113	−	0.476510i
$953$			4.64155e14i			0.590471i	0.955425	+	0.295236i	$0.0953981\pi$
$953$			4.64155e14i			0.590471i	−0.955425	+	0.295236i	$0.904602\pi$
$954$	−1.05059e14	+	2.17218e13i	−0.132951	+	0.0274887i
$955$	−7.09970e14			−0.893764
$956$	−6.15702e14	+	3.55476e14i	−0.771048	+	0.445165i
$957$	−9.29007e12	−	9.08142e13i	−0.0115733	−	0.113134i
$958$	−1.24571e14	+	2.15764e14i	−0.154380	+	0.267393i
$959$	−4.86152e14	−	2.80680e14i	−0.599348	−	0.346034i
$960$	1.15837e14	−	1.18499e13i	0.142067	−	0.0145331i
$961$	2.38391e14	+	4.12906e14i	0.290853	+	0.503772i
$962$		−	5.82217e14i		−	0.706658i
$963$	−1.51771e14	−	5.02468e13i	−0.183255	−	0.0606705i
$964$	5.52075e14			0.663152
$965$	4.52428e14	−	2.61209e14i	0.540645	−	0.312142i
$966$	6.60004e14	+	2.96051e14i	0.784622	+	0.351950i
$967$	−7.35609e14	+	1.27411e15i	−0.869990	+	1.50687i	−0.00798486	+	0.999968i	$0.502542\pi$
$967$	−7.35609e14	+	1.27411e15i	−0.869990	+	1.50687i	−0.862005	+	0.506899i	$0.830792\pi$
$968$	1.34100e14	+	7.74225e13i	0.157780	+	0.0910941i
$969$	9.80397e14	+	1.35731e15i	1.14758	+	1.58877i
$970$	−2.24635e14	−	3.89078e14i	−0.261588	−	0.453084i
$971$			5.54464e14i			0.642358i	0.947019	+	0.321179i	$0.104079\pi$
$971$			5.54464e14i			0.642358i	−0.947019	+	0.321179i	$0.895921\pi$
$972$	2.22101e14	−	3.72644e14i	0.255988	−	0.429500i
$973$	−2.41850e15			−2.77320
$974$	1.26375e13	−	7.29627e12i	0.0144167	−	0.00832350i
$975$	−1.66746e14	+	1.20442e14i	−0.189248	+	0.136696i
$976$	9.70111e11	−	1.68028e12i	0.00109540	−	0.00189729i
$977$	7.40469e14	+	4.27510e14i	0.831829	+	0.480257i	0.854479	−	0.519487i	$-0.173877\pi$
$977$	7.40469e14	+	4.27510e14i	0.831829	+	0.480257i	−0.0226493	+	0.999743i	$0.507210\pi$
$978$	3.14489e13	−	7.01107e13i	0.0351488	−	0.0783592i
$979$	1.32143e14	+	2.28879e14i	0.146937	+	0.254503i
$980$			6.45273e14i			0.713860i
$981$	4.25903e14	−	1.28644e15i	0.468776	−	1.41594i
$982$	1.12787e14			0.123510
$983$	1.11054e15	−	6.41171e14i	1.20995	−	0.698564i	0.247200	−	0.968964i	$-0.420489\pi$
$983$	1.11054e15	−	6.41171e14i	1.20995	−	0.698564i	0.962748	+	0.270401i	$0.0871562\pi$
$984$	1.41379e12	+	1.38204e13i	0.00153253	+	0.0149811i
$985$	−2.40416e14	+	4.16413e14i	−0.259288	+	0.449100i
$986$	−5.47055e13	−	3.15842e13i	−0.0587011	−	0.0338911i
$987$	2.05362e15	−	2.10080e14i	2.19247	−	0.224284i
$988$	3.40022e14	+	5.88935e14i	0.361178	+	0.625579i
$989$		−	3.82449e14i		−	0.404196i
$990$	−1.91482e14	−	9.26113e14i	−0.201350	−	0.973841i
$991$	−1.67995e15			−1.75763			−0.878815	−	0.477163i	$-0.841665\pi$
$991$	−1.67995e15			−1.75763			−0.878815	+	0.477163i	$0.841665\pi$
$992$	9.51163e13	−	5.49154e13i	0.0990140	−	0.0571658i
$993$	−1.23934e15	−	5.55918e14i	−1.28364	−	0.575790i
$994$	7.76948e14	−	1.34571e15i	0.800682	−	1.38682i
$995$	1.54528e15	+	8.92168e14i	1.58450	+	0.914811i
$996$	−4.76522e13	−	6.59721e13i	−0.0486168	−	0.0673076i
$997$	−8.62492e14	−	1.49388e15i	−0.875547	−	1.51649i	−0.856179	−	0.516680i	$-0.827168\pi$
$997$	−8.62492e14	−	1.49388e15i	−0.875547	−	1.51649i	−0.0193683	−	0.999812i	$-0.506166\pi$
$998$		−	9.64630e14i		−	0.974334i
$999$	−3.91435e14	−	1.23976e15i	−0.393398	−	1.24598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.11.d.a.5.2	✓	20
3.2	odd	2		54.11.d.a.17.6		20
9.2	odd	6	inner	18.11.d.a.11.2	yes	20
9.4	even	3		162.11.b.c.161.2		20
9.5	odd	6		162.11.b.c.161.19		20
9.7	even	3		54.11.d.a.35.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.11.d.a.5.2	✓	20	1.1	even	1	trivial
18.11.d.a.11.2	yes	20	9.2	odd	6	inner
54.11.d.a.17.6		20	3.2	odd	2
54.11.d.a.35.6		20	9.7	even	3
162.11.b.c.161.2		20	9.4	even	3
162.11.b.c.161.19		20	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-19.5959 + 11.3137i) q^{2} +(-196.987 + 142.285i) q^{3} +(256.000 - 443.405i) q^{4} +(3091.89 + 1785.10i) q^{5} +(2250.37 - 5016.87i) q^{6} +(12604.4 + 21831.4i) q^{7} +11585.2i q^{8} +(18558.8 - 56056.7i) q^{9} -80784.5 q^{10} +(-171690. + 99125.1i) q^{11} +(12661.4 + 123770. i) q^{12} +(141992. - 245938. i) q^{13} +(-493988. - 285204. i) q^{14} +(-863055. + 88288.4i) q^{15} +(-131072. - 227023. i) q^{16} +1.47323e6i q^{17} +(270534. + 1.30845e6i) q^{18} -4.67704e6 q^{19} +(1.58305e6 - 913972. i) q^{20} +(-5.58918e6 - 2.50709e6i) q^{21} +(2.24294e6 - 3.88489e6i) q^{22} +(4.51953e6 + 2.60935e6i) q^{23} +(-1.64841e6 - 2.28214e6i) q^{24} +(1.49036e6 + 2.58138e6i) q^{25} +6.42584e6i q^{26} +(4.32022e6 + 1.36831e7i) q^{27} +1.29069e7 q^{28} +(1.64106e6 - 947468. i) q^{29} +(1.59135e7 - 1.14944e7i) q^{30} +(9.25805e6 - 1.60354e7i) q^{31} +(5.13695e6 + 2.96582e6i) q^{32} +(1.97166e7 - 4.39553e7i) q^{33} +(-1.66677e7 - 2.88693e7i) q^{34} +9.00003e7i q^{35} +(-2.01048e7 - 2.25796e7i) q^{36} -9.06055e7 q^{37} +(9.16509e7 - 5.29147e7i) q^{38} +(7.02273e6 + 6.86501e7i) q^{39} +(-2.06808e7 + 3.58202e7i) q^{40} +(-4.27366e6 - 2.46740e6i) q^{41} +(1.37890e8 - 1.41058e7i) q^{42} +(-3.66421e7 - 6.34660e7i) q^{43} +1.01504e8i q^{44} +(1.57449e8 - 1.40192e8i) q^{45} -1.18086e8 q^{46} +(-2.91846e8 + 1.68497e8i) q^{47} +(5.81216e7 + 2.60710e7i) q^{48} +(-1.76502e8 + 3.05711e8i) q^{49} +(-5.84101e7 - 3.37231e7i) q^{50} +(-2.09619e8 - 2.90207e8i) q^{51} +(-7.27001e7 - 1.25920e8i) q^{52} +8.02924e7i q^{53} +(-2.39465e8 - 2.19255e8i) q^{54} -7.07793e8 q^{55} +(-2.52922e8 + 1.46025e8i) q^{56} +(9.21316e8 - 6.65475e8i) q^{57} +(-2.14388e7 + 3.71330e7i) q^{58} +(7.95473e8 + 4.59267e8i) q^{59} +(-1.81795e8 + 4.05285e8i) q^{60} +(3.70068e6 + 6.40977e6i) q^{61} +4.18972e8i q^{62} +(1.45772e9 - 3.01396e8i) q^{63} -1.34218e8 q^{64} +(8.78049e8 - 5.06942e8i) q^{65} +(1.10933e8 + 1.08441e9i) q^{66} +(9.55400e8 - 1.65480e9i) q^{67} +(6.53238e8 + 3.77147e8i) q^{68} +(-1.26156e9 + 1.29055e8i) q^{69} +(-1.01824e9 - 1.76364e9i) q^{70} +2.72418e9i q^{71} +(6.49431e8 + 2.15008e8i) q^{72} +2.42985e9 q^{73} +(1.77550e9 - 1.02508e9i) q^{74} +(-6.60875e8 - 2.96442e8i) q^{75} +(-1.19732e9 + 2.07382e9i) q^{76} +(-4.32808e9 - 2.49882e9i) q^{77} +(-9.14303e8 - 1.26581e9i) q^{78} +(7.42978e8 + 1.28688e9i) q^{79} -9.35907e8i q^{80} +(-2.79793e9 - 2.08069e9i) q^{81} +1.11662e8 q^{82} +(-5.66479e8 + 3.27057e8i) q^{83} +(-2.54249e9 + 1.83646e9i) q^{84} +(-2.62987e9 + 4.55506e9i) q^{85} +(1.43607e9 + 8.29117e8i) q^{86} +(-1.88457e8 + 4.20138e8i) q^{87} +(-1.14839e9 - 1.98907e9i) q^{88} -1.33310e9i q^{89} +(-1.49926e9 + 4.52851e9i) q^{90} +7.15890e9 q^{91} +(2.31400e9 - 1.33599e9i) q^{92} +(4.57889e8 + 4.47605e9i) q^{93} +(3.81266e9 - 6.60372e9i) q^{94} +(-1.44609e10 - 8.34899e9i) q^{95} +(-1.43391e9 + 1.46685e8i) q^{96} +(2.78067e9 + 4.81625e9i) q^{97} -7.98759e9i q^{98} +(2.37028e9 + 1.14640e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 84 q^{3} + 5120 q^{4} - 9918 q^{5} + 12864 q^{6} + 12238 q^{7} + 79248 q^{9} - 327582 q^{11} + 9216 q^{12} - 280550 q^{13} + 175680 q^{14} - 2685042 q^{15} - 2621440 q^{16} + 3925632 q^{18} - 2966240 q^{19}+ \cdots + 41160676842 q^{99}+O(q^{100}) \) 20 * q - 84 * q^3 + 5120 * q^4 - 9918 * q^5 + 12864 * q^6 + 12238 * q^7 + 79248 * q^9 - 327582 * q^11 + 9216 * q^12 - 280550 * q^13 + 175680 * q^14 - 2685042 * q^15 - 2621440 * q^16 + 3925632 * q^18 - 2966240 * q^19 - 5078016 * q^20 - 11895726 * q^21 + 3473472 * q^22 + 10446606 * q^23 + 2752512 * q^24 + 9609944 * q^25 + 2340576 * q^27 + 12531712 * q^28 + 32440806 * q^29 + 37556352 * q^30 - 40069958 * q^31 - 35367930 * q^33 + 30746496 * q^34 - 32695296 * q^36 - 127390400 * q^37 + 370567296 * q^38 + 153125550 * q^39 - 245419398 * q^41 - 344505600 * q^42 - 86593094 * q^43 + 394622766 * q^45 - 366913920 * q^46 + 1094979330 * q^47 + 26738688 * q^48 - 598072056 * q^49 - 456606720 * q^50 - 2329772724 * q^51 + 143641600 * q^52 + 1623484224 * q^54 - 262510308 * q^55 + 89948160 * q^56 + 311135772 * q^57 + 249515904 * q^58 - 2125085130 * q^59 - 2357738496 * q^60 + 312021586 * q^61 + 5475513858 * q^63 - 2684354560 * q^64 + 13076821350 * q^65 + 2185467264 * q^66 - 1200881210 * q^67 - 2610487296 * q^68 - 11765922354 * q^69 + 1138681152 * q^70 + 1554382848 * q^72 + 5213376328 * q^73 + 9118122624 * q^74 + 13244996208 * q^75 - 759357440 * q^76 - 33678720774 * q^77 - 14572366080 * q^78 - 3396212726 * q^79 + 14546869128 * q^81 + 3667214592 * q^82 + 16739541378 * q^83 + 1518514176 * q^84 + 7141101588 * q^85 - 11512304064 * q^86 - 32778228834 * q^87 - 1778417664 * q^88 + 16769410560 * q^90 - 10426841884 * q^91 + 5348662272 * q^92 - 4843832814 * q^93 + 6416128320 * q^94 - 26494427340 * q^95 - 1962934272 * q^96 + 6721893598 * q^97 + 41160676842 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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